He has previously played for Partick Thistle, Luton Town and Kilmarnock, and was capped once by the Scotland under-21 team in 2013 before being selected 26 times at full level from 2018, including at the UEFA Euro 2020 tournament.

[13] He made his Luton debut in a 3–1 win at home to newly promoted Championship club Bristol City in the League Cup on 11 August.

[14] O'Donnell's first goal for the club was a 90th-minute winner in a 2–1 win at home to Leyton Orient in the Football League Trophy on 1 September.

[17] However, a loss of form saw O'Donnell lose his place in the team to academy graduate James Justin after a 2–0 defeat away to Crawley Town on 17 September.

[18] He regained his place in the team to make his first league start in five matches after Justin suffered a calf injury in the warm up before Luton's 2–1 win away to Leyton Orient on 15 October.

[19] O'Donnell lost his place once more when Justin returned from injury for Luton's 3–1 win away to Exeter City in the FA Cup on 5 November, but a half-time substitute appearance in the next round at home to National League club Solihull Moors on 3 December saw him score twice as Luton overturned a 2–0 deficit to win 6–2.

[20] He was then recalled to the starting lineup by manager Nathan Jones for the subsequent league match at home to Carlisle United, which resulted in a 1–1 draw.