The Hollywood producer, who wrote scripts and lyrics for the long-running children's show, passed away on 21 January (11) in Valhalla, New York after suffering complications from a neck injury.
Geiss earned 22 Daytime Emmy awards for screenwriting and songwriting over the 30 years he worked on the show, according to the Hollywood Reporter.
He also co-wrote hit 1988 animated dinosaur movie The Land Before Time as well as Steven Spielberg's 1986 film An American Tail.
A statement from Sesame Street bosses reads: "Tony's brilliant words, his sense of humour, his musical virtuosity, and his respect for children in this country and around the world, brought laughter, love and learning together for generations."
Geiss has no immediate survivors; his wife of 60 years, Phyllis Eisen, passed away in 2009.