You just have to set your ListBox HorizontalAlignment to Left, and VerticalAlignment to Top. This should do the trick.
Simple example :
MainWindow.xaml
<Window x:Class="ListBoxFitItemsPanel.MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Title="MainWindow" Height="400" Width="400">
<ListBox ScrollViewer.HorizontalScrollBarVisibility="Disabled" ScrollViewer.VerticalScrollBarVisibility="Disabled" Background="Red" HorizontalAlignment="Left" VerticalAlignment="Top" >
<ListBox.ItemsPanel>
<ItemsPanelTemplate>
<WrapPanel Background="AntiqueWhite" Margin="5" />
</ItemsPanelTemplate>
</ListBox.ItemsPanel>
<Rectangle Width="100" Height="100" Fill="LightSlateGray" Stroke="Black" StrokeThickness="1" Margin="5" />
<Rectangle Width="100" Height="100" Fill="LightSlateGray" Stroke="Black" StrokeThickness="1" Margin="5" />
<Rectangle Width="100" Height="100" Fill="LightSlateGray" Stroke="Black" StrokeThickness="1" Margin="5" />
<Rectangle Width="100" Height="100" Fill="LightSlateGray" Stroke="Black" StrokeThickness="1" Margin="5" />
<Rectangle Width="100" Height="100" Fill="LightSlateGray" Stroke="Black" StrokeThickness="1" Margin="5" />
<Rectangle Width="100" Height="100" Fill="LightSlateGray" Stroke="Black" StrokeThickness="1" Margin="5" />
<Rectangle Width="100" Height="100" Fill="LightSlateGray" Stroke="Black" StrokeThickness="1" Margin="5" />
<Rectangle Width="100" Height="100" Fill="LightSlateGray" Stroke="Black" StrokeThickness="1" Margin="5" />
<Rectangle Width="100" Height="100" Fill="LightSlateGray" Stroke="Black" StrokeThickness="1" Margin="5" />
</ListBox>
</Window>

EDIT : It also works in a Binding scenario :
MainWindow.xaml
<Window x:Class="ListBoxFitItemsPanel.MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:local="clr-namespace:ListBoxFitItemsPanel"
Title="MainWindow" Height="400" Width="400">
<Window.Resources>
<DataTemplate DataType="{x:Type local:Item}">
<Rectangle Width="100" Height="100" Fill="LightSlateGray" Stroke="Black" StrokeThickness="1" Margin="5" />
</DataTemplate>
</Window.Resources>
<ListBox ItemsSource="{Binding Items}" ScrollViewer.HorizontalScrollBarVisibility="Disabled" ScrollViewer.VerticalScrollBarVisibility="Disabled" Background="Red" HorizontalAlignment="Left" VerticalAlignment="Top" >
<ListBox.ItemsPanel>
<ItemsPanelTemplate>
<WrapPanel Background="AntiqueWhite" Margin="5" />
</ItemsPanelTemplate>
</ListBox.ItemsPanel>
</ListBox>
</Window>
MainWindow.xaml.cs
using System.Collections.Generic;
using System.Windows;
namespace ListBoxFitItemsPanel
{
/// <summary>
/// Interaction logic for MainWindow.xaml
/// </summary>
public partial class MainWindow : Window
{
public MainWindow()
{
InitializeComponent();
DataContext = this;
}
public IEnumerable<Item> Items
{
get
{
for (int i = 0; i < 9; i++)
{
yield return new Item();
}
}
}
}
public class Item { }
}