On 25 February 2011, Celtic announced they had secured the signing of Matthews on a pre-contract agreement to commence on 1 July, on a four-year contract. Matthews would team up with his former Cardiff teammate Joe Ledley. Matthews was given the number two shirt that was previously worn by Andreas Hinkel.
Matthews made an impressive debut in a 1–0 win over Aberdeen on 7 August. He then played in his first European match, after coming on as a substitute in Celtic’s 2–0 loss to Atlético Madrid. On 29 September he played in Celtic’s 1–1 Europa League draw with Udinese, he started the match at right back but moved to left back for the second half when fellow countryman Joe Ledley went off injured. After an impressive start to the season, it was reported that English Premier League clubs Fulham and Everton were interested in signing Matthews in the January transfer window. He made his Champions League debut at Celtic Park against HJK Helsinki on 1 August 2012. Matthews scored his first goal Celtic goal on 12 December 2012, a powerful strike into the far corner of the goal against Arbroath in the Scottish Cup replay.