You need to extract the control template and styles of the ScrollBar and adapt them. You can extract them using Visual Studio or Blend. Put them into your application resource dictionary or local control resources, to be able to access them from your ScrollBar. For your custom style adapting the SolidColorBrushes in the extracted assets below should be enough to achieve the desired result.
<Style x:Key="FocusVisual">
<Setter Property="Control.Template">
<Setter.Value>
<ControlTemplate>
<Rectangle Margin="2" StrokeDashArray="1 2" SnapsToDevicePixels="true" StrokeThickness="1" Stroke="{DynamicResource {x:Static SystemColors.ControlTextBrushKey}}"/>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
<SolidColorBrush x:Key="ScrollBar.Static.Background" Color="#F0F0F0"/>
<SolidColorBrush x:Key="ScrollBar.Static.Border" Color="#F0F0F0"/>
<SolidColorBrush x:Key="ScrollBar.Static.Glyph" Color="#606060"/>
<SolidColorBrush x:Key="ScrollBar.Static.Thumb" Color="#CDCDCD"/>
<SolidColorBrush x:Key="ScrollBar.MouseOver.Background" Color="#DADADA"/>
<SolidColorBrush x:Key="ScrollBar.MouseOver.Border" Color="#DADADA"/>
<SolidColorBrush x:Key="ScrollBar.MouseOver.Glyph" Color="#000000"/>
<SolidColorBrush x:Key="ScrollBar.MouseOver.Thumb" Color="#A6A6A6"/>
<SolidColorBrush x:Key="ScrollBar.Pressed.Background" Color="#606060"/>
<SolidColorBrush x:Key="ScrollBar.Pressed.Border" Color="#606060"/>
<SolidColorBrush x:Key="ScrollBar.Pressed.Thumb" Color="#606060"/>
<SolidColorBrush x:Key="ScrollBar.Pressed.Glyph" Color="#FFFFFF"/>
<SolidColorBrush x:Key="ScrollBar.Disabled.Background" Color="#F0F0F0"/>
<SolidColorBrush x:Key="ScrollBar.Disabled.Border" Color="#F0F0F0"/>
<SolidColorBrush x:Key="ScrollBar.Disabled.Glyph" Color="#BFBFBF"/>
<Style x:Key="RepeatButtonTransparent" TargetType="{x:Type RepeatButton}">
<Setter Property="OverridesDefaultStyle" Value="true"/>
<Setter Property="Background" Value="Transparent"/>
<Setter Property="Focusable" Value="false"/>
<Setter Property="IsTabStop" Value="false"/>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="{x:Type RepeatButton}">
<Rectangle Fill="{TemplateBinding Background}" Height="{TemplateBinding Height}" Width="{TemplateBinding Width}"/>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
<Style x:Key="ScrollBarButton" TargetType="{x:Type RepeatButton}">
<Setter Property="FocusVisualStyle" Value="{StaticResource FocusVisual}"/>
<Setter Property="BorderThickness" Value="1"/>
<Setter Property="HorizontalContentAlignment" Value="Center"/>
<Setter Property="VerticalContentAlignment" Value="Center"/>
<Setter Property="Padding" Value="1"/>
<Setter Property="Focusable" Value="false"/>
<Setter Property="IsTabStop" Value="false"/>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="{x:Type RepeatButton}">
<Border x:Name="border" Background="{StaticResource ScrollBar.Static.Background}" BorderThickness="1" BorderBrush="{StaticResource ScrollBar.Static.Border}" SnapsToDevicePixels="true">
<ContentPresenter x:Name="contentPresenter" Focusable="False" HorizontalAlignment="{TemplateBinding HorizontalContentAlignment}" Margin="{TemplateBinding Padding}" SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}" VerticalAlignment="{TemplateBinding VerticalContentAlignment}"/>
</Border>
<ControlTemplate.Triggers>
<Trigger Property="IsMouseOver" Value="true">
<Setter Property="Background" TargetName="border" Value="{StaticResource ScrollBar.MouseOver.Background}"/>
<Setter Property="BorderBrush" TargetName="border" Value="{StaticResource ScrollBar.MouseOver.Border}"/>
</Trigger>
<Trigger Property="IsPressed" Value="true">
<Setter Property="Background" TargetName="border" Value="{StaticResource ScrollBar.Pressed.Background}"/>
<Setter Property="BorderBrush" TargetName="border" Value="{StaticResource ScrollBar.Pressed.Border}"/>
</Trigger>
<Trigger Property="IsEnabled" Value="false">
<Setter Property="Opacity" TargetName="contentPresenter" Value="0.56"/>
<Setter Property="Background" TargetName="border" Value="{StaticResource ScrollBar.Disabled.Background}"/>
<Setter Property="BorderBrush" TargetName="border" Value="{StaticResource ScrollBar.Disabled.Border}"/>
</Trigger>
</ControlTemplate.Triggers>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
<Style x:Key="ScrollBarThumbVertical" TargetType="{x:Type Thumb}">
<Setter Property="OverridesDefaultStyle" Value="true"/>
<Setter Property="IsTabStop" Value="false"/>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="{x:Type Thumb}">
<Rectangle x:Name="rectangle" Fill="{StaticResource ScrollBar.Static.Thumb}" Height="{TemplateBinding Height}" SnapsToDevicePixels="True" Width="{TemplateBinding Width}"/>
<ControlTemplate.Triggers>
<Trigger Property="IsMouseOver" Value="true">
<Setter Property="Fill" TargetName="rectangle" Value="{StaticResource ScrollBar.MouseOver.Thumb}"/>
</Trigger>
<Trigger Property="IsDragging" Value="true">
<Setter Property="Fill" TargetName="rectangle" Value="{StaticResource ScrollBar.Pressed.Thumb}"/>
</Trigger>
</ControlTemplate.Triggers>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
<Style x:Key="ScrollBarThumbHorizontal" TargetType="{x:Type Thumb}">
<Setter Property="OverridesDefaultStyle" Value="true"/>
<Setter Property="IsTabStop" Value="false"/>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="{x:Type Thumb}">
<Rectangle x:Name="rectangle" Fill="{StaticResource ScrollBar.Static.Thumb}" Height="{TemplateBinding Height}" SnapsToDevicePixels="True" Width="{TemplateBinding Width}"/>
<ControlTemplate.Triggers>
<Trigger Property="IsMouseOver" Value="true">
<Setter Property="Fill" TargetName="rectangle" Value="{StaticResource ScrollBar.MouseOver.Thumb}"/>
</Trigger>
<Trigger Property="IsDragging" Value="true">
<Setter Property="Fill" TargetName="rectangle" Value="{StaticResource ScrollBar.Pressed.Thumb}"/>
</Trigger>
</ControlTemplate.Triggers>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
<Style x:Key="ScrollBarStyle" TargetType="{x:Type ScrollBar}">
<Setter Property="Stylus.IsPressAndHoldEnabled" Value="false"/>
<Setter Property="Stylus.IsFlicksEnabled" Value="false"/>
<Setter Property="Background" Value="{StaticResource ScrollBar.Static.Background}"/>
<Setter Property="BorderBrush" Value="{StaticResource ScrollBar.Static.Border}"/>
<Setter Property="Foreground" Value="{DynamicResource {x:Static SystemColors.ControlTextBrushKey}}"/>
<Setter Property="BorderThickness" Value="1,0"/>
<Setter Property="Width" Value="{DynamicResource {x:Static SystemParameters.VerticalScrollBarWidthKey}}"/>
<Setter Property="MinWidth" Value="{DynamicResource {x:Static SystemParameters.VerticalScrollBarWidthKey}}"/>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="{x:Type ScrollBar}">
<Grid x:Name="Bg" SnapsToDevicePixels="true">
<Grid.RowDefinitions>
<RowDefinition MaxHeight="{DynamicResource {x:Static SystemParameters.VerticalScrollBarButtonHeightKey}}"/>
<RowDefinition Height="0.00001*"/>
<RowDefinition MaxHeight="{DynamicResource {x:Static SystemParameters.VerticalScrollBarButtonHeightKey}}"/>
</Grid.RowDefinitions>
<Border Background="{TemplateBinding Background}" BorderThickness="{TemplateBinding BorderThickness}" BorderBrush="{TemplateBinding BorderBrush}" Grid.Row="1"/>
<RepeatButton x:Name="PART_LineUpButton" Command="{x:Static ScrollBar.LineUpCommand}" IsEnabled="{TemplateBinding IsMouseOver}" Style="{StaticResource ScrollBarButton}">
<Path x:Name="ArrowTop" Data="M 0,4 C0,4 0,6 0,6 0,6 3.5,2.5 3.5,2.5 3.5,2.5 7,6 7,6 7,6 7,4 7,4 7,4 3.5,0.5 3.5,0.5 3.5,0.5 0,4 0,4 z" Fill="{StaticResource ScrollBar.Static.Glyph}" Margin="3,4,3,3" Stretch="Uniform"/>
</RepeatButton>
<Track x:Name="PART_Track" IsEnabled="{TemplateBinding IsMouseOver}" IsDirectionReversed="true" Grid.Row="1">
<Track.DecreaseRepeatButton>
<RepeatButton Command="{x:Static ScrollBar.PageUpCommand}" Style="{StaticResource RepeatButtonTransparent}"/>
</Track.DecreaseRepeatButton>
<Track.IncreaseRepeatButton>
<RepeatButton Command="{x:Static ScrollBar.PageDownCommand}" Style="{StaticResource RepeatButtonTransparent}"/>
</Track.IncreaseRepeatButton>
<Track.Thumb>
<Thumb Style="{StaticResource ScrollBarThumbVertical}"/>
</Track.Thumb>
</Track>
<RepeatButton x:Name="PART_LineDownButton" Command="{x:Static ScrollBar.LineDownCommand}" IsEnabled="{TemplateBinding IsMouseOver}" Grid.Row="2" Style="{StaticResource ScrollBarButton}">
<Path x:Name="ArrowBottom" Data="M 0,2.5 C0,2.5 0,0.5 0,0.5 0,0.5 3.5,4 3.5,4 3.5,4 7,0.5 7,0.5 7,0.5 7,2.5 7,2.5 7,2.5 3.5,6 3.5,6 3.5,6 0,2.5 0,2.5 z" Fill="{StaticResource ScrollBar.Static.Glyph}" Margin="3,4,3,3" Stretch="Uniform"/>
</RepeatButton>
</Grid>
<ControlTemplate.Triggers>
<MultiDataTrigger>
<MultiDataTrigger.Conditions>
<Condition Binding="{Binding IsMouseOver, ElementName=PART_LineDownButton}" Value="true"/>
<Condition Binding="{Binding IsPressed, ElementName=PART_LineDownButton}" Value="true"/>
</MultiDataTrigger.Conditions>
<Setter Property="Fill" TargetName="ArrowBottom" Value="{StaticResource ScrollBar.Pressed.Glyph}"/>
</MultiDataTrigger>
<MultiDataTrigger>
<MultiDataTrigger.Conditions>
<Condition Binding="{Binding IsMouseOver, ElementName=PART_LineUpButton}" Value="true"/>
<Condition Binding="{Binding IsPressed, ElementName=PART_LineUpButton}" Value="true"/>
</MultiDataTrigger.Conditions>
<Setter Property="Fill" TargetName="ArrowTop" Value="{StaticResource ScrollBar.Pressed.Glyph}"/>
</MultiDataTrigger>
<MultiDataTrigger>
<MultiDataTrigger.Conditions>
<Condition Binding="{Binding IsMouseOver, ElementName=PART_LineDownButton}" Value="true"/>
<Condition Binding="{Binding IsPressed, ElementName=PART_LineDownButton}" Value="false"/>
</MultiDataTrigger.Conditions>
<Setter Property="Fill" TargetName="ArrowBottom" Value="{StaticResource ScrollBar.MouseOver.Glyph}"/>
</MultiDataTrigger>
<MultiDataTrigger>
<MultiDataTrigger.Conditions>
<Condition Binding="{Binding IsMouseOver, ElementName=PART_LineUpButton}" Value="true"/>
<Condition Binding="{Binding IsPressed, ElementName=PART_LineUpButton}" Value="false"/>
</MultiDataTrigger.Conditions>
<Setter Property="Fill" TargetName="ArrowTop" Value="{StaticResource ScrollBar.MouseOver.Glyph}"/>
</MultiDataTrigger>
<Trigger Property="IsEnabled" Value="false">
<Setter Property="Fill" TargetName="ArrowTop" Value="{StaticResource ScrollBar.Disabled.Glyph}"/>
<Setter Property="Fill" TargetName="ArrowBottom" Value="{StaticResource ScrollBar.Disabled.Glyph}"/>
</Trigger>
</ControlTemplate.Triggers>
</ControlTemplate>
</Setter.Value>
</Setter>
<Style.Triggers>
<Trigger Property="Orientation" Value="Horizontal">
<Setter Property="Width" Value="Auto"/>
<Setter Property="MinWidth" Value="0"/>
<Setter Property="Height" Value="{DynamicResource {x:Static SystemParameters.HorizontalScrollBarHeightKey}}"/>
<Setter Property="MinHeight" Value="{DynamicResource {x:Static SystemParameters.HorizontalScrollBarHeightKey}}"/>
<Setter Property="BorderThickness" Value="0,1"/>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="{x:Type ScrollBar}">
<Grid x:Name="Bg" SnapsToDevicePixels="true">
<Grid.ColumnDefinitions>
<ColumnDefinition MaxWidth="{DynamicResource {x:Static SystemParameters.HorizontalScrollBarButtonWidthKey}}"/>
<ColumnDefinition Width="0.00001*"/>
<ColumnDefinition MaxWidth="{DynamicResource {x:Static SystemParameters.HorizontalScrollBarButtonWidthKey}}"/>
</Grid.ColumnDefinitions>
<Border Background="{TemplateBinding Background}" BorderThickness="{TemplateBinding BorderThickness}" BorderBrush="{TemplateBinding BorderBrush}" Grid.Column="1"/>
<RepeatButton x:Name="PART_LineLeftButton" Command="{x:Static ScrollBar.LineLeftCommand}" IsEnabled="{TemplateBinding IsMouseOver}" Style="{StaticResource ScrollBarButton}">
<Path x:Name="ArrowLeft" Data="M 3.18,7 C3.18,7 5,7 5,7 5,7 1.81,3.5 1.81,3.5 1.81,3.5 5,0 5,0 5,0 3.18,0 3.18,0 3.18,0 0,3.5 0,3.5 0,3.5 3.18,7 3.18,7 z" Fill="{StaticResource ScrollBar.Static.Glyph}" Margin="3" Stretch="Uniform"/>
</RepeatButton>
<Track x:Name="PART_Track" Grid.Column="1" IsEnabled="{TemplateBinding IsMouseOver}">
<Track.DecreaseRepeatButton>
<RepeatButton Command="{x:Static ScrollBar.PageLeftCommand}" Style="{StaticResource RepeatButtonTransparent}"/>
</Track.DecreaseRepeatButton>
<Track.IncreaseRepeatButton>
<RepeatButton Command="{x:Static ScrollBar.PageRightCommand}" Style="{StaticResource RepeatButtonTransparent}"/>
</Track.IncreaseRepeatButton>
<Track.Thumb>
<Thumb Style="{StaticResource ScrollBarThumbHorizontal}"/>
</Track.Thumb>
</Track>
<RepeatButton x:Name="PART_LineRightButton" Command="{x:Static ScrollBar.LineRightCommand}" Grid.Column="2" IsEnabled="{TemplateBinding IsMouseOver}" Style="{StaticResource ScrollBarButton}">
<Path x:Name="ArrowRight" Data="M 1.81,7 C1.81,7 0,7 0,7 0,7 3.18,3.5 3.18,3.5 3.18,3.5 0,0 0,0 0,0 1.81,0 1.81,0 1.81,0 5,3.5 5,3.5 5,3.5 1.81,7 1.81,7 z" Fill="{StaticResource ScrollBar.Static.Glyph}" Margin="3" Stretch="Uniform"/>
</RepeatButton>
</Grid>
<ControlTemplate.Triggers>
<MultiDataTrigger>
<MultiDataTrigger.Conditions>
<Condition Binding="{Binding IsMouseOver, ElementName=PART_LineRightButton}" Value="true"/>
<Condition Binding="{Binding IsPressed, ElementName=PART_LineRightButton}" Value="true"/>
</MultiDataTrigger.Conditions>
<Setter Property="Fill" TargetName="ArrowRight" Value="{StaticResource ScrollBar.Pressed.Glyph}"/>
</MultiDataTrigger>
<MultiDataTrigger>
<MultiDataTrigger.Conditions>
<Condition Binding="{Binding IsMouseOver, ElementName=PART_LineLeftButton}" Value="true"/>
<Condition Binding="{Binding IsPressed, ElementName=PART_LineLeftButton}" Value="true"/>
</MultiDataTrigger.Conditions>
<Setter Property="Fill" TargetName="ArrowLeft" Value="{StaticResource ScrollBar.Pressed.Glyph}"/>
</MultiDataTrigger>
<MultiDataTrigger>
<MultiDataTrigger.Conditions>
<Condition Binding="{Binding IsMouseOver, ElementName=PART_LineRightButton}" Value="true"/>
<Condition Binding="{Binding IsPressed, ElementName=PART_LineRightButton}" Value="false"/>
</MultiDataTrigger.Conditions>
<Setter Property="Fill" TargetName="ArrowRight" Value="{StaticResource ScrollBar.MouseOver.Glyph}"/>
</MultiDataTrigger>
<MultiDataTrigger>
<MultiDataTrigger.Conditions>
<Condition Binding="{Binding IsMouseOver, ElementName=PART_LineLeftButton}" Value="true"/>
<Condition Binding="{Binding IsPressed, ElementName=PART_LineLeftButton}" Value="false"/>
</MultiDataTrigger.Conditions>
<Setter Property="Fill" TargetName="ArrowLeft" Value="{StaticResource ScrollBar.MouseOver.Glyph}"/>
</MultiDataTrigger>
<Trigger Property="IsEnabled" Value="false">
<Setter Property="Fill" TargetName="ArrowLeft" Value="{StaticResource ScrollBar.Disabled.Glyph}"/>
<Setter Property="Fill" TargetName="ArrowRight" Value="{StaticResource ScrollBar.Disabled.Glyph}"/>
</Trigger>
</ControlTemplate.Triggers>
</ControlTemplate>
</Setter.Value>
</Setter>
</Trigger>
</Style.Triggers>
</Style>
Finally, use the control template in your ScrollBar by applying the ScrollBarStyle style.
<ScrollBar x:Name="Scrollbar" Orientation="Vertical" BorderBrush="#FFF72323" SmallChange="0.01" Height="32" Margin="0,16,20,32" VerticalAlignment="Stretch" RenderTransformOrigin="1.471,0.469" HorizontalAlignment="Right" Background="#FFDE7C7C" Foreground="#FFDE2525" OpacityMask="#FFF14949" Style="{DynamicResource ScrollBarStyle}">
<ScrollBar.RenderTransform>
<TransformGroup>
<ScaleTransform/>
<SkewTransform/>
<RotateTransform Angle="180"/>
<TranslateTransform X="-33.014" Y="1.984"/>
</TransformGroup>
</ScrollBar.RenderTransform>
</ScrollBar>
