He also appeared in ITV detective drama Cracker and the James Bond films Goldeneye and The World Is Not Enough.
In a statement, his agent Belinda Wright confirmed the actor died in hospital near Falkirk in Scotland.
She described Coltrane as a “unique talent”, adding his role as Hagrid “brought joy to children and adults alike all over the world”.
“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 called his agent, I shall miss him.
Robbie Coltrane – funny or serious, always compelling
“He is survived by his sister Annie Rae, his children Spencer and Alice and their mother Rhona Gemmell. They would like to thank the medical staff at Forth Valley Royal Hospital in Larbert for their care and diplomacy.
“Please respect Robbie’s family’s privacy at this distressing time.”
Harry Potter author JK Rowling led the tributes on Twitter, describing Coltrane as an “incredible talent”.
Actor Stephen Fry, who appeared alongside Coltrane in Alfresco, tweeted: “Such depth, power, and talent: funny enough to cause helpless hiccups and to honk as we made our first TV show Alfresco. Farewell, old fellow, you’ll be so dreadfully missed.”
Scotland’s first minister Nicola Sturgeon described Coltrane’s death as “very sad news”.
“He had such range and depth as an actor, from brilliant comedy to hard-edged drama. I think my favorite of all his roles was Fitz in Cracker,” she said.
“Robbie Coltrane, Scottish entertainment legend – you will be hugely missed. RIP.”
Coltrane was made an OBE in the 2006 New Year’s honors list for his services to drama and he was awarded the Bafta Scotland Award for outstanding contribution to film in 2011.
The Scottish star, whose real name is Anthony Robert McMillan, was born in Rutherglen, South Lanarkshire, in 1950.
Coltrane was the son of teacher and pianist Jean Ross and GP Ian Baxter McMillan and was educated at the independent school Glenalmond College in Perth and Kinross.
The actor’s career began in 1979 in the TV series Play for Today, but he became prominent in A Kick Up the Eighties, a BBC TV comedy series that also starred Tracey Ullman, Miriam Margoles, and Rik Mayall.
He also appeared in the 1983 ITV comedy Alfresco, with Fry, Emma Thompson, Siobhan Redmond, and Hugh Laurie.
By 1987 he had a leading role in Tutti Frutti, about Scottish rock and roll band The Majestics, which also starred Emma Thompson and Richard Wilson.
Coltrane gained further fame starring as criminal psychologist Dr. Eddie “Fitz” Fitzgerald in the ITV series Cracker from 1993 to 1995 and in a special return episode in 2006.
The role secured him the Bafta award for best actor for three consecutive years from 1994 to 1996.
Arguably his best-known role came in the Harry Potter film series as he starred in all eight movies as Rubeus Hagrid alongside Daniel Radcliffe, Rupert Grint, and Emma Watson.
