McBride, who played for the Hoops between June 1965 and November 1968, passed away at Glasgow Royal Infirmary on Wednesday night having suffered a suspected stroke at the weekend, Celtic confirmed on Thursday morning.
He suffered a mid-season injury which ruled him out of Celtic's 1967 European Cup triumph over Inter Milan in Lisbon, having already scored 35 goals in 26 games during the campaign.
Celtic chief executive Peter Lawwell paid tribute to McBride, who had also worked as an ambassador for the club.
"The passing of Joe McBride is tragic news," he told the club's official website. "Joe was a very fine man, an absolute gentleman and someone who gave tremendous service to the club over a number of years.
"It was a privilege to know Joe and it was fantastic that someone who gave so much to Celtic was still involved with the club in a number of ways - he will truly be sadly missed by everyone at Celtic. The thoughts of everyone at the club are very much with Joe's family at this very difficult time."
The Scotland international had a formidable strike rate during his career, especially whilst at Celtic, where his goalscoring exploits rank amongst the best in the club's illustrious history. McBride started his career with Kilmarnock before an unsuccessful time in England led to him moving to Partick and Motherwell and then on to Celtic.
Great success followed as he won two league championships and a couple of League Cups with the Hoops, scoring 86 goals in 94 games for the club. Former team-mate Tommy Gemmell also paid his respects to the prolific frontman.
"This has come as a terrible shock," he told The Sun. "Joe was a great lad and we had some wonderful moments together. It was easy to see why the Celtic supporters took to him. He was one of their own and a real man's man in the dressing room and out on the pitch.
"Our thoughts immediately go out to his family at this dreadful time."