Try this:

$ git add -u

This tells git to automatically stage tracked files -- including deleting the previously tracked files.

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If you are using git 2.0, you should now use:

$ git add -u :/

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Warning, starting git 2.0 (mid 2013), this will stage files on the whole working tree. If you want to stage file only under your current path with that working tree, then you need to use

$ git add -u .