As David says, mp3wrap is the way to go. However, I found that it didn't fix the audio length header, so iTunes refused to play the whole file even though all the data was there. (I merged three 7-minute files, but it only saw up to the first 7 minutes.)
I dug up this blog post, which explains how to fix this and also how to copy the ID3 tags over from the original files (on its own, mp3wrap deletes your ID3 tags). Or to just copy the tags (using id3cp from id3lib), do:
id3cp original.mp3 new.mp3