Sunderland boss Gus Poyet has admitted that Connor Wickham will be sold unless he commits to a new contract.
Hannover admit to being in the market for a new midfielder but deny that Chelsea's Marko Marin is a target.
The England and Great Britain international agreed a deal with the Sky Bet Championship side earlier in the week but it was only confirmed on Friday to allow him to stay at Elland Road through the end of the play-offs, should Leeds make it into the top six.
Butland spent three months on loan with Barnsley and returned to Stoke in January, where he made two Premier League starts after regular first-choice Asmir Begovic suffered a broken finger.
Boss Mark Hughes feels the move will be beneficial for the 20-year-old, as he said: "Hopefully he can go there, get games and continue his development, because he has had a good year.
"He has been out on loan already, and then played a few Premier League games which was crucial for him.
"Now this opportunity to go to Leeds, where they have a big fanbase and big expectations will be another good step for him."
Butland joins a Leeds team sitting 12th in the table but only eight points off sixth-placed Reading with a game in hand and he should go straight into their squad to face Middlesbrough at the Riverside on Saturday.
Watch coverage of Middlesbrough against Leeds in the Sky Bet Championship on FL72 Live on Sky Sports 1HD from 12pm on Saturday.