Grant Gourlay, 48, was cycling on the A926 between Maryton and Kirriemuir in Angus on Wednesday when he collided with a van. He died at the scene.
Mr Gourlay was a lifelong Celtic fan who had first met McGrain as a schoolboy after writing a letter to Celtic.
He met the defender, who also played for Scotland, several times over the years.
McGrain, who played for Celtic from 1967 to 1987 and is now a coach at the Parkhead club, said: "I'm saddened to hear of Grant's death because he was an extremely nice guy. He was really interested in my career and I found that really humbling.
"I know he had a passion for music and hoped to be a music teacher and I was pleased to hear he achieved his ambitions. My thoughts are with his family."
Mr Gourlay ran his own music school and was well-known in his hometown of Dundee.
In 2005, he played alongside his childhood hero in a charity football match, afterwards describing the experience as "the nearest I will get to Heaven without dying".
Mr Gourlay had also been involved with Dundee Roadrunners.
Earlier, his cousin Stephen Gourlay, 49, had paid tribute, saying: "He was a marvellous cousin, well loved."