He died at lunchtime on Sunday, his son told BBC News.
Lord Attenborough was one of Britain’s leading actors, before becoming a highly successful director.
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 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 6 years ago, our correspondent added.
His family is expected to make a full statement tomorrow.
RIP Richard Attenborough.
"Welcome to Jurassic Park."