He was best known for starring in the original stage production of Hairspray and also appeared in TV series such as The Sopranos and Law & Order.
Marc Shaiman, who wrote the music and co-wrote the lyrics for Hairspray, confirmed the news in a Facebook post.
"Hairspray (and Broadway) has lost a huge piece of its heart. RIP to the glorious, loving and much loved Dick Latessa," he wrote.
"This was a man who defined Pro, with the timing of a Swiss watch and a voice, a smile and sweet soul that made you feel special just to know him. We were lucky to have him in our lives, he was, truly, timeless."
Latessa played the role of Wilbur Turnblad in the original 2002 production of Hairspray, an adaption of the 1988 film.
He went on to win the Tony Award for best featured actor in a musical the following year.
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Tony Award-winning actor Dick Latessa had died at the age of 87.