BioWare and the Star Wars: The Old Republic teams have announced that the initial round of free character transfers has opened up for players. Transfers are free of charge and must occur between approved origin and destination servers.
The character transfer service will be made available gradually, starting with a small number of the lowest population servers and adding more until all servers eligible for transfer are made available in the service. Eligible servers will be listed as they become available for transfers at www.swtor.com/transfer. This is to prevent potential server load issues. As a result, you may have to wait a short period before you can begin your character transfer.
Read more about character transfers on the Star Wars: The Old Republic site.