The Celtic great and Lisbon Lion, who won 18 Scotland caps, died on 2 March after a long illness.
The funeral procession left Celtic Park in the east end of Glasgow shortly after 11:30.
It travelled down the Celtic Way, then on to London Road and towards Daldowie Crematorium for the service.
Fellow members of the Celtic team which won the European Cup in Lisbon in 1967 were among the pallbearers.
They included Bobby Lennox, Bertie Auld, John Clark and Jim Craig, alongside former Rangers and Scotland winger Willie Henderson.
Other former Celtic players at the funeral included Danny McGrain, Andy Walker, Davie Provan and Frank McGarvey, as well as current manager Brendan Rodgers and former boss David Hay.
Rangers managing director Stewart Robertson attended on behalf of the Ibrox club.
Jim Craig spoke at the service of how his former team-mate remained inspirational despite declining health in recent years.
Choking back tears, he said: "That once powerful frame began to weaken and Tam was confined to his bed, a situation such a strong athlete must have found really difficult to cope with.
"Yet, as his strength waned, I never once heard him complain and, frankly, the way he dealt with whatever came his way was a lesson to us all."
Of their playing days together, Jim Craig said: "Tam could be accused of being noisy, argumentative, flamboyant - he had the flashy suits and the car with the Colonel Bogey horn - and even cocky.
"But he also delivered - his scoring record an excellent one for a fullback, and his ability to drive home a penalty a great bonus.
"Probably his most famous goal was the equaliser in the European Cup Final, although with great modesty might I point out that he received such a perfect pass along the 18-yard line that his granny could have knocked that one in."
Former footballer Tommy Gemmell, who died last week aged 73, has been described as "an inspiration" at his funeral service.