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.