The Scottish star, whose real name is Anthony Robert McMillan, was best known for playing the beloved Hogwarts gamekeeper Hagrid and starring as criminal psychologist Dr Eddie "Fitz" Fitzgerald in British crime drama Cracker.
His agent of 40 years Belinda Wright said Coltrane died on Friday and thanked the medical staff at Forth Valley Royal Hospital in Larbert, near Falkirk in Scotland for their "care and diplomacy".
"Robbie was a unique talent, sharing the Guinness Book of Records' Award for winning three consecutive Best Actor Baftas for his portrayal of Fitz in Granada TV's series Cracker in 1994/1995/and 1996 with Sir Michael Gambon," she said.
"He will probably be best remembered for decades to come as Hagrid in the Harry Potter films.
"A role which brought joy to children and adults alike all over the world prompting a stream of fan letters every week for over 20 years.
"James Bond fans write too to applaud his role in GoldenEye and The World Is Not Enough.
"For me personally, I shall remember him as an abidingly loyal client as well as being a wonderful actor, he was forensically intelligent, brilliantly witty and after 40 years of being proud to be to called his agent, I shall miss him."
Coltrane was made an OBE in the 2006 New Year's honours list for his services to drama and he was awarded the Bafta Scotland Award for outstanding contribution to film in 2011.
The actor is survived by his sister Annie Rae, his children Spencer and Alice and their mother Rhona Gemmell.
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