Viola arrived in Los Angeles after World War II as a member of the Page Cavanaugh Trio abd eventually became a prominent studio musician, the Los Angeles Times said Friday.
"He was a chameleon and could play in any style -- that was his great talent," jazz singer Judy Chamberlain told the Times. "You could barely see his hands move, he was so smooth and quick with his fingers."
Viola, whose work with Sinatra spanned 25 years, can be heard on such Sinatra hits as "Witchcraft," "All the Way," "My Way" and "New York, New York."
Besides his mandolin work on "The Godfather" theme, Viola's soundtrack credits included "West Side Story," "Who's Afraid of Virginia Woolf?" and "Blazing Saddles."
Viola, who died Wednesday, is survived by his wife, two sons and a granddaughter.