A Celtic academy graduate, McGregor has spent his entire professional career at the club, except for a single season on loan at Notts County in 2013–14.

McGregor particularly cites a conversation with Burns as a 13-year old as staying with him throughout his whole career, where he urged him to match his ability with the correct attitude and a desire to prove himself.

[12] McGregor's loan expired at the start of January 2014, with his 12 goals in all competitions making him the current top scorer for Notts County at that stage.

[16] McGregor was put straight to the Notts County squad for their game against Walsall and marked his return with a goal, a 25-yard free kick into the top left corner.

[19] McGregor credits the loan spell for allowing him to develop as a player and learn the game, and felt that being involved in a relegation battle where his teammate's livelihoods were on the line caused him to "grow up a bit".

[20] McGregor made his first team debut for Celtic against KR Reykjavík on 15 July 2014 in a Champions League qualifier and he scored the only goal of the game.

[25][26] In the 2017 Scottish Cup Final, he started in his usual midfield position but played the majority of the match at left back after an injury to Kieran Tierney.

[27] Having previously been on target in qualifying matches, on 31 October 2017 McGregor scored his first goal in the group stages of the Champions League, striking the equaliser at home to Bayern Munich (James Forrest providing the assist), although the German team responded to claim a 2–1 win.

[28] Celtic then dropped into the 2017–18 UEFA Europa League, in which McGregor scored the only goal in the first leg of the last-32 tie with Zenit St Petersburg.

In 2020–21 the club lost control of all three trophies and did not win any of their matches against Rangers, with McGregor scoring an own goal in one visit to Ibrox Stadium[38] and being sent off in the first half of another.

"[43] On 20 July 2021, in his first competitive appearance as club captain, McGregor was awarded Man of the Match in a 1–1 draw against FC Midtjylland in the UEFA Champions League Second qualifying round.

[50] In October 2017, McGregor was once again included in the full squad for two 2018 World Cup qualifiers against Slovakia and Slovenia, but remained on the bench during both games.

[58] In February 2016, McGregor was stopped by the police and charged with driving under the influence of alcohol, having already been convicted and banned for speeding the previous year; he was later disqualified for 12 months.