He died March 9 in in his longtime Central Park West apartment, his daughter, Lucia, told The New York Times.
Coppola worked with his nephew as a conductor on 1990's The Godfather: Part III leading "Cavalleria Rusticana" and 1992's Bram Stoker's Dracula.
He appeared on a 2015 episode of Mozart in the Jungle, the Amazon series created by his great nephews Roman Coppola a son of Francis and Jason Schwartzman a son of Francis' sister, Talia. He was also a great-uncle to actor Nicolas Cage and writer-director Sofia Coppola.
On Broadway starting in 1947, Coppola worked as musical director on such productions as Carmen, Madame Butterfly, Aida, La Boheme and The Barber of Seville. He received a Tony Award nomination in 1963 for best conductor and musical director for Bravo Giovanni.
He conducted for the New York Philharmonic and the New York City Opera and worked on a 1954 national tour of The Boy Friend, in which Julie Andrews made her American debut.
Coppola joined Opera Tampa in 1996 and served in an artistic director position until he retired in April 2012 at age 95.
"I think one of the things that keeps conductors going is that we have to exercise our mental powers all the time," he told the St. Petersburg Times in 2004. "Doing that, I think, contributes to your physical well-being. I mean, I'm constantly using my mind to absorb these scores that I conduct.
And in 2016 interview with The New York Times, he said: "I'm not tired yet. When people ask me how did I live this long, I say, 'Pasta e fagioli.'"
Born in New York, Coppola was raised as one of seven brothers in East Harlem. One of his brothers, Carmine, also wrote music for Francis' films.
After serving in the U.S. Army as a bandmaster during World War II, he worked as a conductor at Radio City Music Hall and was the director of the symphony and opera departments at the Manhattan School of Music for 15 years.
Coppola married a ballet dancer, Almerinda Drago, in the late 1940s, and they had two children, Bruno and Lucia. He had lived in his Central Park West apartment since 1956.