Son Clark Tracey said the musician "passed away peacefully" yesterday. He had been suffering from cancer.
London-born Tracey began playing piano during World War II after a stint as an accordionist. He went on to perform with the popular Ted Heath Orchestra and spent several years as resident pianist at Ronnie Scott's jazz club.
His compositions included the "Under Milk Wood" suite, based on the Dylan Thomas radio play.
A mentor to many younger musicians, Tracey became known as "the godfather of British jazz" and released his final album earlier this year.