The 32-year-old, who arrived at Leeds on a free transfer from Northampton in the summer of 2009, has not featured for United this season.
Crowe said: "The last few months have been tough, but I can also look back on some real highlights while I've been here."
Crowe, who started out as a trainee at Arsenal and had spells at Portsmouth and Grimsby, made a total of 27 appearances for Leeds.
He added: "I'm disappointed things haven't worked out, but I'm looking forward to a new challenge now and I can't wait to get playing again."