He died of oesophageal cancer at his Florida home, the New York Times said, quoting his wife, the writer Isabel Fonseca.
Amis is best known for his 1984 novel Money and the 1989 work London Fields.
He authored 14 novels and several non-fiction books, and is widely considered one of the most influential writers of his era.
Born in 1949 in Oxford, he was the son of the novelist and poet Sir Kingsley Amis.
The younger Amis followed in his father's footsteps after graduating from Oxford University with his first novel The Rachel Papers.
Published in 1973 while he was working at the Times Literary Supplement, it follows the romantic exploits of a teenage boy in London before university and - like his father's debut novel - won the Somerset Maugham Award for fiction.
Amis was a contemporary of other celebrated writers like James Fenton, Salman Rushdie, and Ian McEwan.
His close relationship with the journalist Christopher Hitchens, who died of oesophageal cancer in 2011, was well-documented.
They belonged to a colourful set which reinvigorated the British literary scene and has been credited with inspiring a generation of younger writers.
Rushdie paid tribute to Amis, telling the New Yorker: "He used to say that what he wanted to do was leave behind a shelf of books - to be able to say, 'from here to here, it's me'.
"His voice is silent now. His friends will miss him terribly. But we have the shelf."
And another contemporary, Sir Kazuo Ishiguro, told the BBC: "He was a standard-bearer for my generation of novelists and an inspiration to me personally.
"For all the bite of his satire, the brilliant swagger of his prose, there was always something tender not far from the surface, a yearning for love and connection. His work will last, surviving the various shifts of fashions and mores."