I have an FAA ATPL based on a foreign ATPL, can I convert it to an EASA ATPL?
Do you actually have an ATPL or a frozen ATPL? 

Essentially, EASA requires you to sit all the ATPLs as well as the individual IR exam and your practical flight tests for the CPL, ME and IR. That is conditional on you having completed an "approved course of training" and whether your FAA stuff counts I don't know; I doubt it as it isn't EASA. 
Some stuff (CPL, ME &amp; IR) can be converted depending on experience but from what I understand from a friend, many UK schools are very reluctant to do this at all. I can't speak for other EASA nations.

So essentially, plan on doing your ATPL again.