Bennett sold millions of records around the world, and picked up 20 Grammys during his career, including a lifetime achievement award.
Recognised as one of America’s last great crooners, Bennett performed with a number of musical legends, from Frank Sinatra to Lady Gaga.
His first album was released in 1952 while Bennett was in his mid-20s and has charted in the US in every decade since its release.
Publicist Sylvia Weiner confirmed Bennett’s death to The Associated Press, saying he died in his hometown of New York.
There was no specific cause, but Bennett had been diagnosed with Alzheimer’s disease in 2016.
The last of the great saloon singers of the mid-20th century, Bennett often said his lifelong ambition was to create “a hit catalogue rather than hit records”.
He released more than 70 albums, bringing him 19 competitive Grammys, all but two after he reached his 60s, and enjoyed deep and lasting affection from fans and fellow artists.
Bennett performed his final show in 2016 alongside Lady Gaga.