Sullivan made the drop from the Premiership in order to regain first-team football after languishing in the reserves at Stamford Bridge.
He said: "It is a great move for me because it gives me an opportunity to start playing again. That was my number one aim and hopefully things will work out well for me at Leeds."
Sullivan, bought on a free transfer, has signed a two-year contract and goes into the season as first choice but also to bring along second choice Scott Carson.
He told the club's official website: "I heard about Scotty and everyone here says what great potential he has.
"Now if I can help him out in any way and help him to develop that will be great for Leeds.
"To be honest I think that's part of why the manager brought me here, to pass on a few tips if I can and help him improve.
"I will be glad of that until he takes my place and then it will be a different matter!"