Yes, I just did it. I haven't actually got the license in my hands yet, but it's waiting for me at the FSDO in Fort Lauderdale, I'm assured.
Whole process took 10 days. Very efficient.
There are two forms you need to fill in:
Send this one to the FAA
The instructions on the FAA website are here including all the links you'll need.
Send this form to the CAA with £15
When they notify you that the checks are complete, you can collect your temporary license from the FSDO you nominated. You apply for the permanent one at the FSDO. As I say, I haven't done this yet, so I'll let you know how it goes in mid February.
Don't forget that to 'activate' your new license, you'll need to do a full Biennial Flight Review with an FAA instructor. As far as I know, this still doesn't count as training, so no visa is requirted (as long as you don't do any other training, obviously).
Good luck.