The realist painter, one of Britain's most popular and highly celebrated artists, died at his London home after an illness.
Freud was the grandson of the psycho-analyst Sigmund Freud. He was born in Berlin in 1922, and moved to Britain with his family at the age of 10 in 1933.
New York dealer William Acquavella announced the news of his death, and described him as "one of the great painters of the 20th Century".
"In company he was exciting, humble, warm and witty," he added. "He lived to paint and painted until the day he died, far removed from the noise of the art world."
Tate gallery director Nicholas Serota said: "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.
"His early paintings redefined British art and his later works stand comparison with the great figurative painters of any period."
Freud's works have been highly sought after in recent years, including a painting of an overweight nude woman sleeping on a sofa, which was sold in 2008 for $33.6m (£20.6m).
