Doing so in the past would have been painful and given you a lot of bad geometry. If you tried to animate it you'd get horrible mesh deformations.
Now, you might be able to get good results with the intersect tool added in 2.71.
Here's a YouTube video about how to use it:
Basically you tell Blender to calculate the intersection of the two meshes, then delete the over lap, and finally you can bridge the two in a number of different ways (including the bridge tool, but in your case probably merging each vertex pair).
There might still be some odd topology to clean up, and it might not animate cleanly.. but I think cleaning this up will be easier than other methods of getting the vertices in the same place.