McNeill was born in Bellshill. He played for nearby club Blantyre Victoria before signing for Celtic in 1957. During his playing career at Celtic, McNeill was the captain of the clubs most successful sides of the 1960s and 1970s. In his 18 seasons at the club, Celtic won many honours. This totalled nine league titles, seven Scottish Cups, six Scottish League Cups and one European Cup. In the 1966–67 season, Celtic won the European Cup Final against Inter Milan, with McNeill as captain. This was the first European Cup won by a British side, and the only to date won by a Scottish side. Celtic again made the European Cup Final in 1970. However, McNeill's side lost to Feyenoord.