The fiery midfielder, who stood just 5 foot 3 inches tall, made his debut for the Hoops as an 18-year-old in 1949 and went on to score 116 goals in 320 games over the next nine years before moving to Everton for a club record fee of £23,500.
During his time with Celtic he was capped 16 times by the Scottish League and won the first of his 31 caps at full international level in 1950 aged just 19.
Collins, nicknamed The Wee Barra, remained on Merseyside for four years, scoring almost a goal every three games in his 133 appearances before Don Revie signed him for the then Second Division side Leeds for a £25,000 fee.
Glasgow-born Collins made 167 appearances during a five-year stay at Elland Road, picked up the coveted Footballer of the Year award in 1965 and was widely regarded as one of the most influential members of the team which laid the foundations for the club's success in the following years.
Speaking on Leeds' website, fellow Scot and former team-mate Eddie Gray said: "In my opinion Bobby Collins was probably the most influential player in the history of Leeds United. He will be sadly missed by all who knew him and played with him."
Scotland legend Billy Bremner, who replaced Collins as captain of Leeds, once said of his team-mate: "They say one man doesn't make a team, but Bobby Collins came nearer to doing it than anyone else I have ever seen."
In a statement on their website, Celtic said: "Bobby Collins was a true Celtic legend and one of Scotland's all-time great players. His contribution to the success of both Celtic and Leeds United is testament to that.
"The thoughts and prayers of everyone at Celtic are with Bobby's family and friends at this very sad time."
And Everton chairman Bill Kenwright paid tribute to the man he labelled 'an inspiration during his time at Goodison Park'.
"I am extremely saddened to hear of the death of one of my idols Bobby Collins," he said. "Jimmy Lumsden called me to say Bobby's wife had asked him to pass on the sad news as Everton was very much part of Bobby's life.
"Bobby was very much a part of Everton's life and helped transform the club from the minute he arrived at Goodison Park in 1958 as our record signing.
"He was pivotal and ispirational during his four seasons with the Blues and will never be forgotten by our fans and everyone at Everton football club."
Collins, who retired from playing early in 1974 after spells with Bury, Morton, Oldham and Shamrock Rovers, turned his hand to management at Huddersfield, Hull and Barnsley before calling it a day in the late 1990s following a spell coaching Leeds' youth teams.