Grayson said: "Micky brings experience, knowledge and quality. He's played over 200 games in the Championship, captained Coventry and brings a know-how that I think it will be important to us this season."
The Irishman is surplus to requirements at the Ricoh Arena following the arrival of summer recruits Sammy Clingan and Michael McIndoe and has opted for regular football in League One.
Sky Blues boss Chris Coleman explained: "We talked to Michael last season and said that maybe it was time for a change for both parties. He wasn't going to figure as much as last season. He has two years left on his contract and he wants to play and when the Leeds proposition came about he felt it was good for him and we felt it was good for us."