Coltrane also played a former KGB agent-turned-Russian mafia boss in two James Bond films -- "Goldeneye" (1995) and "The World Is Not Enough" (1999) -- with Pierce Brosnan.
British actor Daniel Radcliffe, who played the role of Harry Potter, and JK Rowling, the author of Harry Potter books, shared heartfelt tributes remembering the late Coltrane.
Radcliffe said, "Robbie was one of the funniest people I've met and used to keep us laughing constantly as kids on the set".
Coltrane and Radcliffe starred together in all eight 'Harry Potter' movies, right from the 'Sorcerer's Stone' in 2001 to 'Death Hallows - Part 2' in 2011.
"I feel incredibly lucky that I got to meet and work with him and very sad that he's passed. He was an incredible actor and a lovely man." Radcliffe said.
Rowling separately honoured Coltrane with a post on Twitter, writing, "I'll never know anyone remotely like Robbie again. He was an incredible talent, a complete one-off, and I was beyond fortunate to know him, work with him and laugh my head off with him. I send my love and deepest condolences to his family, above all his children."
Coltrane, who was born Anthony Robert McMillan on March 30, 1950, in Rutherglen, near Glasgow, forged a career as an actor, comedian and writer.
Coltrane is survived by his children Spencer and Alice and their mother Rhona Gemmell.
No cause of death was given, but his agent Belinda Wright thanked the medical staff at Forth Valley Royal Hospital in Larbert, central Scotland, "for their care and diplomacy".