[5] A member of the club's under-20 squad[6] McGhee made his first team debut[7] aged 16,[8] on 4 May 2013, coming on as an 86th-minute substitute at Tynecastle in a Scottish Premier League match against St Mirren, replacing Mehdi Taouil in a 3–0 win.

[9] The following season on 24 August 2013, in only his second substitute appearance,[10] he scored his first professional goal,[11] an 88th-minute winner in a 2–1 win over Aberdeen in the Scottish Premiership.

[19] He made his debut two days later on 2 September 2017, starting at centre-back as his new side defeated Sligo Rovers in the Challenge Cup 2–1.

[24] In his second season with Dundee, McGhee would be employed further up the pitch as a box-to-box midfielder by manager James McPake and would find success in this role.

[38] McGhee would lift silverware at the end of the season as Dundee would win the Scottish Championship title on the last day away to Queens Park.

[42] McGhee's purple patch was stopped by a calf injury sidelining him for several weeks, before returning off the bench in another win over St Johnstone.

[43][44] Returning to his traditional place at centre back, McGhee scored his first goal of the season on 17 August 2024 in a dominant League Cup knockout victory over Airdrieonians.

After establishing himself as a regular at centre back alongside Stuart Findlay, he captained the Scotland under-21 side for the first time in a friendly against Switzerland on 18 November 2014 which ended in a 1–1 draw.