The midfielder, whose current deal at stadiummk was due to expire, was offered a new contract by the Club but has instead opted to seek pastures new by penning a two-year-deal with the Blues.
Gleeson’s move to the Midlands ends his five-year spell in Milton Keynes.
Speaking to mkdons.com, Dons boss Karl Robinson said: “I’m gutted he’s gone. We did everything to try and keep him, but he wanted to play in the Championship, which is where we all want to be.
“He’s a good lad and I wish him and his family all the best with the move.”
A product of Wolverhampton Wanderers’ academy, Gleeson initially joined the Dons on loan from the Midlands outfit during the 2008/09 season and impressed enough in his five appearances to earn a permanent move to MK1 that summer.
The former Republic of Ireland international quickly established himself as a first-choice centre midfielder and in July 2011, Karl Robinson named him the Club’s vice-captain.
In total, Gleeson made 206 appearances, scoring 17 goals whilst also helping the side reach the League 1 play-offs three times.
In 2011/12, the influential midfielder was named as one of League 1’s top ten players by opposition managers and was included in the PFA League 1 Team of the Year as he helped the men from MK1 reach the play-offs for a second successive year.
The following campaign saw Gleeson miss considerable time due to injury although he did score a 30-yard screamer in the historic victory over AFC Wimbledon, a strike which would later be awarded Goal of the Season.
Last season, Gleeson made 42 appearances, which saw him pass the 200-mark for MK Dons and contribute three more goals, including a stunner away at Crawley Town on Boxing Day.
MK Dons would like to thank Stephen for his outstanding contribution to the Football Club and wish him every success for the future.