Doyle, who was one of City's longest servants, having joined the club from Celtic in 2003 after impressing in trials for City Reserves, was out of contract at the end of this season and had been told that he was not getting a new deal.
"We wish Michael all the best. I cannot fault his attitude since I have been at the club, particularly when he was out of the side for a long period, said Aidy Boothroyd to Sky Blue Player.
"We have other options in midfield and this was a better long term option for Michael so he goes with our blessing."