Conway was 85.
He had been battling a longtime illness prior to his death, Howard Bragman, Conway's representative, told us. He was not suffering from dementia or Alzheimer's disease, Bragman said.
Conway won three Emmys for co-starring in "The Carol Burnett Show," which ran from 1967 to 1978, and a fourth as a member of its writing team. He also briefly headlined his own variety series and co-starred in several Disney live-action comedies during the '70s, such as "The Apple Dumpling Gang" and "The Shaggy D.A."
In his later years, Conway did numerous guest appearances -- winning additional Emmys for roles in the sitcoms "Coach" and "30 Rock" -- and voiceover work in animation, including "SpongeBob Squarepants."
Conway's improvisational antics frequently cracked up his co-stars, foremost among them Harvey Korman.
"I'm heartbroken. He was one in a million, not only as a brilliant comedian but as a loving human being," Burnett said about Conway in a statement on Tuesday. "I cherish the times we had together both on the screen and off. He'll be in my heart forever."
Burnett will dedicate a previously scheduled performance of her one-woman show, "An Evening of Laughter and Reflection Where the Audience Asks Questions," to Conway's memory on Tuesday night in North Carolina.
Conway's longtime colleague, Vicki Lawrence, also paid tribute.
"Hysterical, crazy, bold, fearless, humble, kind, adorable... all synonyms for Tim Conway," Lawrence said in a statement. "I am so lucky to ever have shared a stage with him. Harvey and Tim are together again...the angels are laughing out loud tonight."
Conway was married twice, first to Mary Anne Dalton from 1961 to 1978 and together they had six children. He is survived by his wife of more than 30 years, Charlene Fusco.
The family has asked that instead of gifts, donations be made to The Lou Ruvo Brain Center at the Cleveland Clinic in Las Vegas, Nevada...