He was born on 16 February 1931 in Govanhill, Renfrewshire, Scotland, the eldest of Tom and Bella Collins's six children. He signed a contract with Everton from Pollok at the age of 17, but after a contractual dispute with Celtic he eventually ended up joining Celtic instead of Everton; he was also working as an apprentice cobbler at the time. He made his debut at outside-right against Old Firm rivals Rangers on 13 August 1949, getting the better of Jock Shaw he helped Celtic to a 3–2 Scottish League Cup victory. Despite being just about 5 ft 3 in (1.60 m) tall, Collins was a strong, hard-working midfield player who was in the Celtic team as a 17-year-old and stayed there for ten years, winning the Scottish Cup in 1951, and the Scottish cup double in 1954. He was also called up for international duty in 1950, and maintained a frequent presence in the Scotland squad in the later stages of the decade. Collins also represented the Scottish League XI 16 times, scoring 12 goals.
In 1958 he joined Everton where he played until 1962. He was an astute addition to the Leeds squad by manager Don Revie in 1962, helping the club avoid relegation. Leeds won promotion to the First Division in 1964, and Collins captained the side towards a potential League and FA Cup double a year later; however, Leeds missed out on the League on goal average to Manchester United, and lost the 1965 FA Cup Final to Liverpool. Collins's efforts in Leeds achievements were recognised as he was awarded the Footballer of the Year title in 1965. His sparkling form at Leeds also won him a recall to the Scotland squad after a 6-year absence, and he earned three more caps. His international career ended with 31 appearances and ten goals. Collins continued to skipper Leeds until 1966, when he suffered a horrific broken thighbone in a Fairs Cup tie against Torino. He briefly came back from the injury, but age and a struggle to reclaim previous form brought his Leeds career to an end.
Bury signed Collins and he stayed there for two years. During a short period back in his native Scotland with Greenock Morton, he doubled up as a scout for Revie, and recommended Joe Jordan. Jordan went on to become a respected and feared striker with Leeds, Manchester United, Milan and Scotland. In 1972 Collins was playing coach of Australian club Ringwood City but left after a disagreement with the club board. He then had a spell as player/coach with Oldham. Collins signed for Shamrock Rovers in November 1973 making his début on the 11th at Glenmalure Park. He played a total of 13 games, 11 in the league scoring once on his second appearance at Finn Harps.