McGinn signed for Celtic on 1 January 2009. On 12 September 2009, McGinn made his first team debut for Celtic against Dundee United. Although the game ended in a 1–1 draw, McGinn was awarded the official Man of the Match award. On 17 September 2009, McGinn made his Europa League Groupstage debut in a 2–1 loss against Hapoel Tel Aviv. In the last Groupstage game with Celtic out, they faced Austrian side Rapid Wien to finished third place. The match ended 3–3 which Celtic finished third. During the match, McGinn started the match and provided assist for Marc-Antoine Fortuné to score the second goal in a match before coming off for Graham Carey.
On 31 October 2009, McGinn scored his first goal for Celtic coming on as a 66th-minute substitute in a 3–0 win over Kilmarnock at Celtic Park. McGinn scored his second goal for Celtic against Hamilton Academical on 26 December 2009 by driving a right footed shot into the top corner. He scored his first goal in the Scottish Cup and his third of the 2009–10 season to put Celtic 1–0 ahead against Greenock Morton on 19 January 2010. In the January transfer window, McGinn was a transfer target for Premier League side Wigan Athletic but wished to stay at Celtic. At the end of the season, McGinn suffered an injury during the end of the last training session of the season on 17 May 2010 after breaking a metatarsal bone in his right foot and out for 2 months. After recovering from his injury, McGinn says manager Neil Lennon played a big role in helping him recover from his injury.
After being on the substitute twice in the game but did not come on, McGinn scored in his first game of the 2010–11 season, a 3–2 win over St Johnstone in the Scottish League Cup on 27 October 2010 which he scored twice in the match. 3 days later on 30 October 2010, McGinn scored twice against them but this time in the league in a 3–2 win. In the next match against Aberdeen, McGinn provided assist for Gary Hooper to score his second in the match which later Hooper scored a hat-trick. That match would hold the record as the biggest ever win in the SPL, as well as being the biggest ever defeat in the history of Aberdeen. Later on the season, McGinn would play less and be on the substitute bench.
Before the start of the season rumours flowed that there was a fall-out between McGinn and Lennon with McGinn being unhappy over being left out of the pre-season tour of Australia. Lennon denied this and explained the leaving out of McGinn was due to his international commitments at the Nations Cup in May. McGinn signed a new one-year extension on his contract at the start of the 2011–12 season before moving to Brentford. After his loan move to Brentford, McGinn says moving to Brentford could be an end of his Celtic career after a phone-call conversation from Lennon.