Brought up in Rutherglen, he lived there for most of his life and attended St. Columbkillle’s Primary school in Rutherglen, before moving to Our Lady’s High Secondary in Motherwell. Murdoch first joined Celtic in 1959, earning £3 per week as a part-time player while also being employed as a sheet-metal worker. He played for junior club Cambuslang Rangers for two years to gain experience before joining Celtic as a full-time professional.
Murdoch initially played for Celtic as an inside right, but only showed signs of being a reasonable performer in that position. This was in a period where players were not well developed by Celtic due to a lack of quality coaching. Jock Stein moved Murdoch to right half soon after he was appointed Celtic manager in 1965. With that simple action, Murdoch was the first player to significantly benefit from Stein’s arrival. Playing in the deeper position allowed Murdoch to use his long passing ability more effectively. He still continued to score at least 10 goals a season, knocking in shots from cutbacks by Bertie Auld or Jimmy Johnstone.
During his time at Celtic, he won eight Scottish League titles, four Scottish Cups and five League Cups, as well as the 1967 European Cup Final winners’ medal. Murdoch’s shot was deflected by Stevie Chalmers to score Celtic’s winning goal. Murdoch also played in the 1970 European Cup Final, when Celtic lost 2–1 to Feyenoord. In total, he made nearly 500 appearances for Celtic and scored approximately 100 goals.
His later years with Celtic were marked with injury problems, as Murdoch had difficulty maintaining his weight at a correct level. His importance to the success of a great Celtic team was such that when Jock Stein was asked when he thought Celtic might win the European Cup again he replied “when Bobby Murdoch is fit”. Stein also credited Murdoch with being “just about the best player I had as a manager”. Murdoch was voted Scottish player of the year in 1969 by the football writers. Stein allowed Murdoch to leave the club because he had “run out of challenges” at Celtic.