His son told the BBC that Lord Attenborough died at lunchtime on Sunday.
After a highly-successful career spanning six decades, he was well-known for his roles in films such as Brighton Rock, The Great Escape and Jurassic Park.
British Prime Minister David Cameron posted on Twitter: “His acting in Brighton Rock was brilliant, his directing of Gandhi was stunning – Richard Attenborough was one of the greats of cinema.”
Attenborough’s family is expected to make a statement on Monday.