As per the EGit User Guide, to use the merge tool, one should right-click on the resource with a merge conflict and then select Team > Merge Tool
This also happens if you're in detached head state (in my case, I had checked out a remote branch and then forgotten).
Also, even after you've corrected the problem, you may have to select a different project and then reselect the one you actually want (just selecting in the package explorer view) in order for the menu to update.