News of the actor’s death was confirmed by his daughter Allegra Okarmus.
Joseph starred in the mob drama in 1999, appearing in flashback scenes that portrayed main character Tony’s troubled relationship with his parents.
As well as his role in The Sopranos, he was known for appearing in the award-winning stage musical Jersey Boys, clocking up 2,000 performances as the character Gyp DeCarlo in the first national tour of the musical from 2006 onwards.
Other TV work included playing Fred Goldman, father of the murdered waiter Ronald Goldman, in 2016′s The People v OJ Simpson – part of the American Crime Story TV series.
His daughter, who was with the star when he died, shared a series of images on Instagram on Sunday.
She wrote: “I was by his side when my dear father passed away this morning, peacefully, in his beloved Treehouse.
“We are both so lucky to be so intensely loved. I am so immensely grateful to have had him here on earth and I know that he hasn’t gone very far. He had many credits, but his favourite one by far was that of Nonno Joe.”
Former co-stars have been paying tribute, including Garry Pastore, who also appeared in The Sopranos in 2004.
Sharing a photo of Joseph from his Instagram page, he wrote: “RIP my dear friend, who fought an incredible fight. I will miss you. See you on the other side.”
He added: “He was a true gent to boot and as you well know hard to find that mutual bond and sincerity. Acting has always been a passion and finding true friends that lift you up and support was often difficult.
“Myself, Joe, Michael Rispoli and Jimmy Gandolfini always supported each other even when up for the same roles, it’s how we rolled.”
Fellow Sopranos star Maureen Van Zandt shared a photo of Joseph on Twitter.
She wrote: “Just heard Joe passed away. A talented and lovely man. A perfect Johnny Boy Soprano. Took this at the workshop of Piece of My Heart, [Broadway] show about Bert Berns. Deepest condolences to his family and friends.”
The Sopranos starred the late James Gandolfini as lead Tony Soprano, running for six seasons from 1999 to 2007, winning multiple Emmy and Golden Globe awards.