Nicholas died Tuesday at his home in Toluca Lake, Calif., the Los Angeles Times reported Thursday. A friend said he had been in poor health since a stroke in November.
Fayard and his younger brother Harold, who died in 2000, were considered Hollywood's greatest dance team, the Times said.
Ballet's Mikhail Baryshnikov once called them "the most amazing dancers I have ever seen in my life -- ever." Fred Astaire said their "Jumpin' Jive" scene in 1943's "Stormy Weather" was the greatest dance number ever filmed.
The brothers began on the vaudeville stage as children and tapped their way to Harlem's legendary Cotton Club, to Broadway and finally, Los Angeles, where they became Hollywood stars of the 1930s and 1940s.
The brothers lived on opposite coasts in the 1960s as they pursued individual careers. Fayard Nicholas acted in the 1970 film "The Liberation of L.B. Jones" and won a Tony in 1989 for his choreography for the Broadway revue "Black and Blue."
He is survived by his third wife, Katherine Hopkins-Nicholas, a sister, two sons, four grandchildren and a great-granddaughter.