On 16 January 2015, Mackay-Steven signed a pre-contract agreement to join Celtic at the end of the season on the expiry of his Dundee United contract. In the January transfer window, he had been pursued by Nigel Clough, manager of English League One club Sheffield United, who made three bids up to £100,000 while Dundee United wanted a minimum of £250,000. On the transfer deadline day, 2 February, Celtic made an offer of £250,000 and the move was completed immediately, with his Dundee United teammate Stuart Armstrong joining in a separate deal at the same time. Five days later, the pair watched from the stands as Celtic won 2–0 at Dundee F.C. in the fifth round of the Scottish Cup.
Mackay-Steven made his debut on 11 February away to Partick Thistle, scoring after 37 seconds in a 3–0 victory. His first goal at Celtic Park came on 1 March as the third in a 4–0 win over Aberdeen, with a shot from 20 yards. On 15 March Celtic won the Scottish League Cup Final against Dundee United, but Mackay-Steven was cup-tied, having already represented Dundee United in the tournament that season.