Having signed a pre-contract agreement with Celtic on 7 January 2011, Wilson officially joined the club on 1 July 2011. Celtic manager Neil Lennon had played alongside Wilson during Lennon’s brief spell at Forest in 2007. Lennon said about Wilson, “I like him a lot. I played with him for six months when I was at Forest. He was 22 then and still developing physically. We have watched him for the last couple of years and he has been very consistent in the Championship”, adding “He’s very quick, composed on the ball and decent in the air as well”.
Wilson made his debut for Celtic in their opening match of the 2011–12 Scottish Premier League, a 2–0 win over Hibernian. He gave a strong performance, making two crucial interventions which denied Hibs goalscoring opportunities and kept Celtic’s 1–0 lead intact. He played in Celtic’s next two matches as they beat Aberdeen 1–0, then Dundee United 5–1. He was due to start in Celtic’s first European match of the season against FC Sion on 13 August, but picked up a leg injury in the build-up to the match, which ended 0–0. This injury kept him out of Celtic’s next two matches, both of which ended in defeat. He made his return on 28 August in a 2–0 win over St Mirren. He then made his European debut in a 2–0 loss to Atlético Madrid at the Vicente Calderón. On 18 September Wilson played in Celtic’s 4–2 defeat against Old Firm rivals Rangers and was responsible for the first goal. His poor clearance allowed Steven Naismith to put Rangers in the lead.