After some trouble, Blizzard have now enabled free transfers from Season of Mastery for EU servers as well, with the US transfers having started a few days ago. Remember that if you do not transfer your characters by the time Season of Mastery realms close (the date¬†hasn’t been announced yet) you will permanently lose them.¬†

Transfers (Source)

Season of Mastery players can now transfer their characters for free to a Classic Era realm or to a Wrath Classic realm of the same ruleset (Normal or PvP).

Please be advised that this transfer is one way only and final. Your decision cannot be changed or reversed.