On 14 August 2015, after one season with Hibs, Allan signed a four-year deal with Scottish Premiership champions Celtic. He made his debut on 22 August, coming on as a substitute during the second half of Celtic’s 3–1 league win away at Dundee United. Allan made his Celtic Park debut, with 10 minutes remaining, in a 3–1 defeat of St Johnstone a week later. He made his first start on 10 December, playing 73 minutes in a 1–1 draw at Fenerbahçe in the UEFA Europa League. Allan did not make his first league start for Celtic until 26 February, in a 1–1 draw at Hamilton. His only other start for the team was a defeat at St Johnstone on 11 May.
Despite being mainly used as substitute throughout his first season, Allan managed to register assists in wins at Inverness on 29 November and Stranraer on 11 January, and also made three more assists at home to Hamilton on 19 January and Inverness on 20 Ferburay. Allan made 17 appearances in all competitions for Celtic during the 2015–16 season. His 13 appearances in the league was enough to qualify him for a winner’s medal, after Celtic won the Scottish Premiership title.