Coltrane’s agent Belinda Wright confirmed the actor had died in hospital in Scotland on Friday (October 15), having been in ill health for two years.
She said: "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.
"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."
Fans gather at Hogwarts Castle in Robbie Coltrane tribute
Among further tributes was a statement from fellow Harry Potter star Daniel Radcliffe, who described Coltrane as “one of the funniest people I’ve ever met” who used to “keep us laughing constantly as kids on set”.
"I’ve especially fond memories of him keeping our spirits up on Prisoner of Azkaban, when we were all hiding from the torrential rain for hours in Hagrid’s hut and he was telling stories and cracking jokes to keep morale up,” Radcliffe added.
"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."
She paid tribute to Coltrane on an Instagram story stating that he "made it a joy to be Hermione" and there was “no better Hagrid”.
"I’ll really miss your sweetness, your nicknames, your warmth, your laughs and your hugs,” she added.
And Rupert Grint, who played Ron, said he was ‘heartbroken’ at the news.
He posted on Instagram: “I’ll never forget the smell of cigars and beard glue- a wonderful combination. No one else on this planet could of played Hagrid, only Robbie.
“Just as Hagrid was in the books and films Robbie was in life- warm, compassionate and hilarious. A giant hearted man who was still looking out for us even decades later. Sending love to his family. See you on the other side Bobser.”
Harry Potter author JK Rowling posted on her Twitter account: “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.”
Who was Robbie Coltrane?
Coltrane, whose real name was Anthony Robert McMillan, was born in Rutherglen, South Lanarkshire, in 1950.
His career began in 1979 in the TV series Play for Today before he gained prominence in A Kick Up the Eighties, a BBC TV comedy series in which he starred alongside Tracey Ullman, Rik Mayall and Miriam Margoyles.
Coltrane went on to appear in the 1983 ITV comedy Alfresco, with Stephen Fry, Emma Thompson, Hugh Laurie and Siobhan Redmond.
Fry tweeted: "Such depth, power and talent: funny enough to cause helpless hiccups and honking as we made our first TV show Alfresco. Farewell, old fellow, you’ll be so dreadfully missed."