In 1956, he started his senior career with Hamilton Academical. He made more than 125 league appearances for Hamilton before leaving in 1960 to join Clyde. After playing in over 100 league games for Clyde, McLean was transferred to Dundee for £10,000 in 1965. This move meant him becoming a full-time professional footballer for the first time in his career, aged 27. His debut for Dundee came at Dens Park on 11 September 1965 when Dundee were beaten 5–0 by Dundee United, their heaviest ever defeat in a Dundee derby. In his first season with Dundee, McLean scored eight goals, and he became their principal threat in attack after Charlie Cooke was sold to Chelsea in April 1966. McLean scored 17 goals for Dundee during the 1966–67 season, which made him the club's leading scorer. He followed this by scoring 18 goals in the 1967–68 season, during which Dundee reached the Scottish League Cup final (losing 5–3 to Celtic) and the Fairs Cup semi-final (losing 2–1 on aggregate to Leeds United).