Avery had recently undergone surgery for an undisclosed illness and died Tuesday, the celebrity website said.
"Fresh Prince" co-star Alfonso Ribeiro posted a message on Twitter saying, "The world has lost a very sepcial man.
"He was a second father to me," Ribeiro said. "I will miss him greatly."
A native of Atlantic City, N.J., Avery served in the U.S. Navy and began his entertainment career in San Diego, CNN reported.
One of the classically trained actor's earliest screen roles was an uncredited turn in the 1980 comedy "The Blues Brothers."
"I knew I loved the arts," Avery said in an interview for the show "Unscripted," CNN reported. "I knew I wanted to be a writer, but the theater was something I had been involved in before."
Avery's credits included extensive voice over work, including as Shredder in the "Teenage Mutant Ninja Turtles."
He became a star as Uncle Phil to Will Smith's character on "The Fresh Prince of Bel-Air."
Celebrity Families of 2014 [PHOTOS]