Publicist Sylvia Weiner confirmed Bennett died on Friday in his hometown of New York - two weeks short of his birthday.
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 didn't tell his own story when performing; he let the music speak instead - the Gershwins and Cole Porter, Irving Berlin and Jerome Kern.
Unlike his friend and mentor Sinatra, he would interpret a song rather than embody it.
If his singing and public life lacked the high drama of Sinatra's, Bennett appealed with an easy, courtly manner and an uncommonly rich and durable voice - "A tenor who sings like a baritone," he called himself - that made him a master of caressing a ballad or brightening an up-tempo number.
"I enjoy entertaining the audience, making them forget their problems," he told The Associated Press in 2006.
"I think people ... are touched if they hear something that's sincere and honest and maybe has a little sense of humour. ... I just like to make people feel good when I perform."
Bennett was praised often by his peers, but never more meaningfully than by what Sinatra said in a 1965 Life magazine interview.
"For my money, Tony Bennett is the best singer in the business," Sinatra said.
"He excites me when I watch him.
"He moves me.
"He's the singer who gets across what the composer has in mind, and probably a little more."
He not only survived the rise of rock music but endured so long and so well he gained new fans and collaborators, some young enough to be his grandchildren.
In 2014, at age 88, Bennett broke his own record as the oldest living performer with a No.1 album on the Billboard 200 chart for Cheek to Cheek, his duets project with Lady Gaga.
Three years earlier, he topped the charts with Duets II, featuring such contemporary stars as Gaga, Carrie Underwood and Amy Winehouse, in her last studio recording.
His rapport with Winehouse was captured in the Oscar-nominated documentary Amy, which showed Bennett patiently encouraging the insecure young singer through a performance of Body and Soul.
