The transformation process can be initiated at us.battle.net. It only takes a few minutes and is relatively painless. Converting your account to Battle.net is not required at this time, but I don't think anyone should be surprised if it is soon.
Malkorix has said that there are problems, and they are aware of the problems, but don't have any ETA on a fix at this time. He also makes a point to note that converting your account to Battle.net is only a reported and unconfirmed by Blizzard solution. However we can say that we haven't seen any issues with Battle.net accounts.
We'll update this post when we have more information.
Update: The issue is fixed, for now.