Thurso-born Mackay-Steven formerly played for Ross County, Liverpool, Airdrie United and Dundee United before joining Celtic in January 2015.
Mackay-Steven becomes Aberdeen's fifth signing of the summer so far.
A farewell ceremony will take place after the final whistle which will mark the club's past, present and future.
Former midfielder Mackay, who passed away in 2015, is regarded as one of the club's greatest ever players and played a key role in the double-winning team of 1961.
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