The star had been suffering from cancer, a statement said.
He became one of Britain’s best-loved acting stars thanks to roles including Professor Snape in the Harry Potter films and Hans Gruber in Die Hard.
Tributes have come from figures like Sense and Sensibility director Ang Lee, who called him “a great human being”.
He was also a “brilliant actor [and] a soulful actor”, according to Lee, who cast Rickman opposite Kate Winslet in the 1995 film.
Sir Michael Gambon, who appeared with Alan Rickman in Harry Potter as well as on stage, told BBC Radio 4 he was “a great friend”.
He added: “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.”
Actor Richard E Grant wrote on Twitter: “Farewell my friend. Your kindness and generosity ever since we met in LA in 1987 and ever since is incalculable.”
Harry Potter actor James Phelps, who played Fred Weasley, said on Twitter he was “shocked and sad” to hear the news. He wrote: “One of the nicest actors I’ve ever met. Thoughts and prayers with his family at this time.”
His twin brother Oliver Phelps, who played George Weasley, added: “Terribly sad news about the passing of Alan Rickman. A funny and engaging person who put a shy young actor at ease when I was on Harry Potter.”
TV star and Bafta ceremony host Stephen Fry wrote: “What desperately sad news about Alan Rickman. A man of such talent, wicked charm and stunning screen and stage presence. He’ll be sorely missed.”
Actor David Morrissey also paid tribute. He said: “So sad to hear the news of Alan Rickman. A wonderful actor and lovely man. Tragic news.”
The London-born star began his career in theatre, including with the Royal Shakespeare Company, before winning roles in TV dramas like Smiley’s People and The Barchester Chronicles in the 1980s.
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His performance as the manipulative seducer Le Vicomte in Les Liaisons Dangereuses on Broadway in 1986 brought him the first of two Tony Award nominations.
It also brought him to the attention of Die Hard producer Joel Silver, who offered him his film debut as a result.
He went on to become best known for playing screen villains – including the Sheriff of Nottingham in 1991’s Robin Hood: Prince of Thieves, for which he won a Bafta award, and Judge Turpin opposite Johnny Depp in 2007’s Sweeney Todd: The Demon Barber of Fleet Street.
But he showed his gentler side in films like 1990’s Truly Madly Deeply, in which he played Juliet Stevenson’s ghost lover and which also earned him a Bafta nomination.
Further Bafta nominations came for his roles as Colonel Brandon in Sense and Sensibility and the calculating Eamon de Valera in 1996’s Michael Collins.
The following year, he won a Golden Globe for best actor in a miniseries or television film for the title role in Rasputin: Dark Servant of Destiny.
Meanwhile, he continued to be a major presence on the stage in London and New York.
Another Tony nomination came for Private Lives in 2002, in which he appeared opposite Lindsay Duncan on Broadway following a transfer from London.
He recently revealed he had married Rima Horton in secret last year. The couple had been together since he was just 19 and she was 18.
Announcing his death on Thursday, a family statement said: “The actor and director Alan Rickman has died from cancer at the age of 69. He was surrounded by family and friends.”