Logan has put pen to paper on a two-year deal that will see him become a permanent member of the Dons' first team squad at the start of July.
The right-back had a very successful loan spell with the Dons, where he helped the club win the Scottish League Cup and finish third in the SPFL Premiership.
Manager Derek McInnes told RedWeb: "We're really pleased to get Shay. I thought he showed enough in his loan spell with us last season in terms of his qualities and we're just looking for that consistency of performance going forward.
"We're delighted he sees Aberdeen as the place to play his football and we're looking forward to working with him again."
Watch Shay's stuner at Celtic Park!