McLeish spent the majority of his first two seasons at Aberdeen in the reserves and also had a loan spell at local Junior side Lewis United. He made his competitive debut under Billy McNeill in a New Year fixture against Dundee United on 2 January 1978. His first major final appearance was under the management of Alex Ferguson as a substitute in a 2–1 defeat to Rangers in the 1978–79 League Cup and most of his appearances during the 1970s were as a midfielder, with Willie Garner and Doug Rougvie preferred in defence. However McLeish eventually made the centre-back position his own, and over the next seven seasons he enjoyed great success, winning eight domestic and two European trophies. Highlights included scoring in a 4–1 victory over Rangers in the 1982 Scottish Cup Final on his 200th Dons appearance, and a vital goal against Bayern Munich during the campaign leading to the European Cup Winners' Cup win over Real Madrid in 1983.