The 27-year-old has agreed to join the Sky Blues on a free transfer when his current deal with Birmingham City concludes at the end of the month.
McSheffrey spent the last three months of the campaign on loan at Elland Road and was rumoured to be keen on joining the Whites in the summer.
McSheffrey made ten appearances for United and scored his only goal for the club against Walsall at the end of January when his cross-come-shot beat Clayton Ince in the Walsall goal.
A number of below par performances saw him dropped to the bench after the Southampton game in mid-March.
And he made just one substitute appearance in the last ten games of the season in Leeds' penultimate home game against MK Dons.