The 36-year-old joined the Black Cats from Preston in 2017 but wasn’t offered a new deal at the Stadium of Light following the end of his contract this summer with Alex Neil’s side clinching promotion to the Championship.
McGeady has been strongly linked with a move to the Scottish Premiership side with that move now being confirmed.
In their first season working together, McGeady excelled under Johnson with the 41-year-old bringing him back into the fold after being exiled by former Cats boss Phil Parkinson.
McGeady went on to be named in the 2020/21 League One team of the year after contributing six goals and 17 assists for Johnson’s side who were beaten in the play-off semi-final by Lincoln City.
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The Irishman struggled with injury last season but was still able to make 16 appearances for the club who achieved promotion in the play-off final against Wycombe Wanderers.
“Aiden is a top player, has had a fantastic career to date, and we aim to extend and accentuate his abilities within the blend of our new-look squad,” said Johnson.
“We will also look to utilise Aiden’s fantastic leadership qualities to help guide and get the best out of our young forward players.”
McGeady returns to the Scottish Premiership 12 years after leaving Glasgow giants Celtic where he enjoyed six years of his career.