The singer was a prolific performer in the 1930s and 1950s, and continued his career in music and television through to the 21st century.
Martin passed away from natural causes on Friday (July 27) at his West Los Angeles home, his friend Beverly Scott stated.
He emerged into the public eye at the same time as the likes of Bing Crosby and Frank Sinatra, and was known for his strong baritone vocals.
His hits included 'I Get Ideas', 'Begin the Beguine' and 'There's No Tomorrow'.
"He's the ultimate crooner who outlasted all his contemporaries," said musician and long-time friend Gabriel Guerrero.
"He has truly remained the butterscotch baritone until he was 98."
Tony Martin appeared in 25 movies during his career, most of which were around the height of Hollywood musicals.
He wed two musical stars - Alice Faye and Cyd Charisse - with the latter marriage lasting for 60 years until her death in 2008.
His 1946 recording of 'To Each His Own' sold over a million copies.
Martin's final film role was 1982's Dear Mr Wonderful starring Joe Pesci.
Watch Tony Martin perform 'All the Things You Are' below: