The midfielder has gone on a season long loan after playing nearly 300 games for City whom he joined from Celtic in 2003.
Leeds manager Simon Grayson told his club's website: "Micky brings experience, knowledge and quality, and he is a good addition to our squad. "He's played over 300 games in the Championship, captained Coventry, and brings a know-how that I think it will be important to us this season."