He was 88.
The grandson of psycho-analyst Sigmund Freud moved to England with his Jewish family in 1933 and became a British citizen in 1939, the BBC said.
He studied at the Central School of Art in London, then the East Anglian School of Painting and Drawing and London's Goldsmiths College.
The artist's depiction of a large nude woman sleeping on a couch sold in 2008 for $33.6 million and set a world record for a work by a living artist, the British broadcaster noted.
"The vitality of [Freud's] nudes, the intensity of the still life paintings and the presence of his portraits of family and friends guarantee Lucian Freud a unique place in the pantheon of late 20th Century art," Nicholas Serota, director of the Tate gallery, told the BBC. "His early paintings redefined British art and his later works stand comparison with the great figurative painters of any period."