As far as I am aware the @Nonnull is there for tooling such as IDE's and to be honest I tend not to bother with it.
I would say its not strictly possible in Java, though there is nothing stopping you coming up with your own annotations, at which point it would only be useful to you and your team unless you updated the tooling (IDE's etc) to understand your annotation.
If you were to use a language like Swift or Kotlin by default val types can not be null, if you wish a val type to except null you add a ? to it to indicate it could possible be null in value.
Personally I use the JavaDoc to explain when I expect something to reject null on input, and when it will return null. Though with Java 8 if i expect a method to return null, I will use Optional to indicate a value may or may not be returned.