Lord Attenborough, who moved to a care home in 2008, died at lunchtime on Sunday aged 90.
Bafta described its former president as a "titan of British cinema" who set an example of "industry, skill and compassion" that business would do well to live up to. His career highlights included appearing in 1993 blockbuster Jurassic Park and clinching eight Oscars for 1982 film Gandhi, including best film and best director.
As an actor he was respected enough for top directors Satyajit Ray and Steven Spielberg to lure him out of self-imposed retirement to appear respectively in The Chess Players and Jurassic Park. Jurassic Park director Spielberg said: "Dickie Attenborough was passionate about everything in his life - family, friends, country and career. He made a gift to the world with his emotional epic Gandhi and he was the perfect ringmaster to bring the dinosaurs back to life as John Hammond in Jurassic Park."
Star of Gandhi Sir Ben Kingsley said he had grown to love the director, who had worked tirelessly to bring the Indian leader's story to the big screen.
"I along with millions of others whom he touched through his life and work will miss him dearly."
Prime Minister David Cameron said: "His acting in Brighton Rock was brilliant, his directing of Gandhi was stunning - Richard Attenborough was one of the greats of cinema," he said.
Labour leader Ed Miliband said: "The death of Richard Attenborough is a sad day for the film world and the Labour movement. He and his work will be remembered." Former prime minister Tony Blair said: "Dickie was someone it was a privilege to know, someone I looked up to and respected.
"Fabulously successful yet humble and utterly without arrogance of any kind; possessing enormous compassion and humanity; gifted, creative, fascinating and yet approachable and good fun."
Actors including Mia Farrow, Sir Roger Moore and Samantha Bond were also quick to praise the supremely talented film legend, a star in front and behind the camera. Actress Farrow tweeted: "Richard Attenborough was the kindest man I have ever had the privilege of working with. A Prince. RIP 'Pa' - and thank you". Sir Roger added: "Greatly saddened to hear the great Richard Attenborough has left us. Such a wonderful and talented man." BFI chief executive Amanda Nevill said: "The world has lost a very, very special person."
Lord Attenborough's beloved Chelsea Football Club said it was "deeply saddened" to learn of the death of the actor and would "always be grateful" that the club was close to his heart."