I recently went from UK ATPL to FAA ATP.
The requirement was to pay the UK CAA some money along with a completed licence verification form (FAA do verifications online free of charge....CAA take note!), complete the verification request form with FAA who will then verifly your licence with the UK CAA. When they have done so, they will mail you a document recognising your UK licence. Then you sit the FAA ATP written exam (needs about 12 days study of a GLEIM course to get through quickly, available online; for FAA CPL, you must print out the clearance form to take the test from within the GLEIM software). An FAA medical exam is to be completed, then a flight test in the aircraft type/category that you require. All fairly straight forward, and in general, the FAA are much easier to deal with than the UK CAA. They are even friendly and there was no charge for my ATP licence issue!
Good luck.