Earlier today via the official forums, Eric Musco dropped by to let players in the APAC region know exactly when they can transfer their characters.
Quote from EricMusco
I know you have been waiting a bit for an update and I wanted to pop in and do exactly that. Starting on Tuesday, June 4th, you will all be allowed a free one time transfer for each character you have on an APAC server. In the last update I gave I told all of you that we were expanding where your one-time transfer could go to include all NA-West servers. After seeing quite a few requests to expand it further, we are going to allow you a one-time transfer to any SWTOR server. To reiterate, starting on Tuesday, June 4th, you will be allowed a one-time transfer for each character you have on an APAC server to any other non-APAC server.