In a career that spanned six decades, he appeared in films including Brighton Rock, World War Two prisoner of war thriller The Great Escape and later in dinosaur blockbuster Jurassic Park.
As a director he was perhaps best known for Gandhi, which won him two Oscars.
Lord Attenborough had been in a nursing home with his wife for a number of years, BBC arts editor Will Gompertz said.
He had also been in a wheelchair since falling down stairs six years ago, our correspondent added.
His son told the BBC that Lord Attenborough died at lunchtime on Sunday.
His family is expected to make a full statement on Monday.
Paying tribute, Prime Minister David Cameron tweeted: “His acting in “Brighton Rock” was brilliant, his directing of “Gandhi” was stunning – Richard Attenborough was one of the greats of cinema.”
Actress Mia Farrow tweeted: “Richard Attenborough was the kindest man I have ever had the privilege of working with. A Prince. RIP ‘Pa’ – and thank you.”
Chris Hewitt from Empire Magazine told BBC News Lord Attenborough had a “huge impact” on cinema, describing him as a “universally beloved” figure.
Along with his naturalist brother David, Lord Attenborough was one of Britain’s best-known screen celebrities.
Born in Cambridge in 1923, he started acting at the age of just 12, making his professional stage debut aged 18.
He was appointed a CBE in 1967 and knighted nine years later in 1976, before being made a life peer in 1993.
He married his wife, actress Sheila Sim, in 1945. His son Michael was born in 1949, followed by two daughters, Jane and Charlotte.
Michael is a theatre director and former artistic director of the Almeida Theatre in Islington, north London, and Charlotte is an actress.
His family faced tragedy in 2004 when his elder daughter Jane Holland, her daughter, Lucy, and her mother-in-law, also named Jane, were killed in the south Asian tsunami on Boxing Day.
Source : BBC News