The robust way to do this is to use a refactoring tool. They know the syntax of the language, so they understand the concept of "assignment statement" and can correctly select the entire expression on either side of the assignment operator rather than be limited to a single identifier, which is what I think all the regular expressions so far have covered. Refactoring tools treat your code as structured code instead of just text. I found mention two Visual Studio add-ins that can do it:
(Inverting assignment isn't technically refactoring since it changes the behavior of the program, but most refactoring tools extend the meaning to include other generic code modifications like that.)
