It's possible if both accounts are in your name. You have to phone customer support though.
I deleted my post since I read the OP.
I know the Battle Tag is not only for Diablo but used across all Blizzard games.
However, was THIS thread created specifically for Diablo 3 players?
Nope this thread is for all bnet games
Feel free to add me
Battle Tag: Pitbull#2123
Started with Hearthstone recently, and seriously looking into getting Heroes of the Storm in the not-so-distant future.