The former Scotland left-back died at the age of 73 after a long illness, Celtic announced last week.
His funeral is being held at Daldowie Crematorium in Uddingston, South Lanarkshire.
Ahead of the service, fans lined the entrance to the Celtic Park ground as the funeral cortege made its way past, allowing them to say their final farewells to the club legend.
Applause rang out as the procession left the Parkhead stadium in the east end of Glasgow for the final time while a number of supporters threw Celtic scarves towards the funeral cars.
A wreath of white flowers beside the coffin bore the emblem of the Lisbon Lions - the Celtic team whose victory over Inter Milan in the Portuguese capital in 1967 saw them become the first British club to win the European Cup.