In May 1983, Billy McNeill signed McClair for Celtic, with the fee being £100,000. McClair was effectively signed as a replacement for the recently departed Charlie Nicholas. However, McClair would never actually play for McNeill, as the Celtic manager resigned in June 1983 and was replaced by Davie Hay.
McClair scored in a 2–0 win on his debut against Partick Thistle at Firhill in the Glasgow Cup on 9 August 1983. By the end of an impressive first season at Celtic, McClair had scored 32 goals and established himself as a first team regular. A four-goal haul against Dundee in a 6–2 win during September, an outstanding solo goal in a 5–0 win over Sporting Lisbon in the UEFA Cup, and a goal in the 2–3 defeat against Rangers in the League Cup Final in March 1984 highlighted McClair’s goalscoring ability.
The following season saw the arrival of Mo Johnston from Watford and, despite their contrasting personalities, McClair and Johnston would quickly form a deadly goalscoring partnership for Celtic. McClair continued to score regularly for Celtic, and at the end of the season won his first winner’s medal, coming on as a substitute in Celtic’s 2–1 win over Dundee United in the 1985 Scottish Cup Final.
Despite competition from Alan McInally and Mark McGhee, McClair and Johnston remained the regular pairing playing up front for Celtic. Their goals helped Celtic to a dramatic league championship win in 1985–86; a memorable 5–0 win over St Mirren at Love Street on the last day of the season with McClair and Johnston both scoring twice as title-rivals Hearts capitulated to a 2–0 defeat at Dundee.
Season 1986–87 would be McClair’s last at Celtic. Despite a bright start to the season from Celtic, the team’s form began to fade during the winter months and the club would go on to squander a nine-point lead in the league, which was eventually won by Rangers. Another league cup final defeat against Rangers (despite an outstanding goal by McClair) and a fourth-round defeat at Hearts in the Scottish Cup saw Celtic finish the season without any silverware. Despite Celtic’s lack of achievement, McClair was an outstanding success that year. He scored 41 goals in total, finishing top scorer in the league with 35 goals and won both the Scottish Football Writers’ Association Player of the Year and the Scottish Players’ Player of the Year awards.
In four seasons with at Celtic, McClair made 204 appearances in all competitions and scored 126 goals. He won the Scottish Cup 1985 and the Scottish Premier Division in 1986.