The British actor, who is best known for playing Severus Snape in the Harry Potter franchise as well as films such as Die Hard and Robin Hood: Prince of Thieves is also known for his work on stage.
Emma Thompson wrote a heartfelt tribute to her friend and Love Actually co-star in Newsweek, calling him the "ultimate ally" and a "rare and unique human being".
She said writing a tribute is hard as the actor was her friend who she has "just kissed goodbye".
"What I remember most in this moment of painful leave-taking is his humour, intelligence, wisdom and kindness. His capacity to fell you with a look or lift you with a word. The intransigence which made him the great artist he was—his ineffable and cynical wit, the clarity with which he saw most things, including me, and the fact that he never spared me the view. I learned a lot from him."
Calling him the "ultimate ally in life, art and politics", Thompson said she "trusted him absolutely".
"He was, above all things, a rare and unique human being and we shall not see his like again."
Sir Michael Gambon, who starred alongside Rickman when he portrayed Professor Dumbledore, told BBC Radio 4 he was a "great friend".
"Everybody loved Alan. He was always happy and fun and creative and very, very funny. He had a great voice, he spoke wonderfully well.
"He was intelligent, he wrote plays, he directed a play. So he was a real man of the theatre and the stage and that's how I think of Alan."
Emma Watson, who played Hermoine Granger in the film series, posted a tribute on her Facebook page calling Rickman "a special man and actor".
I'm very sad to hear about Alan today. I feel so lucky to have worked and spent time with such a special man and actor. I'll really miss our conversations. RIP Alan. We love you
Stephen Fry took to Twitter to express his sadness, writing that he was a man of "such talent and wicked charm".
The leader of the Labour party called him "one of the greatest actors of his generation", as did the former Foreign Secretary David Miliband who called him both a "giant and a gent".
Eddie Izzard and Piers Morgan pointed out that this sad news comes just two days after David Bowie, another iconic British entertainer, died from cancer.
Alan Rickman: Life in pictures
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Fellow Harry Potter actors Oliver and James Phelps who played Fred and George, the identical twins of the Weasley family, also paid tribute. Oliver credited him for putting him at ease when he was a "shy, young actor" while James called him "one of the nicest actors" he'd ever met.
Others from the entertainment and film industries posted tributes to an actor whose first big role on-screen was at the age of 41 in Die Hard.
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