Sedaka, whose hits included Breaking Up Is Hard to Do and Laugher in the Rain, died on Saturday AEDT.
"Our family is devastated by the sudden passing of our beloved husband, father and grandfather, Neil Sedaka," his family said in a statement.
"A true rock and roll legend, an inspiration to millions, but most importantly, at least to those of us who were lucky enough to know him, an incredible human being who will be deeply missed."
No other details of his death were immediately available.
A key member of the Brill Building songwriting factory, Sedaka teamed with lyricist and boyhood neighbour Howard Greenfield on songs that reflected the teen innocence of the post-Elvis/pre-Beatles era of the late 1950s-early 1960s, including Happy Birthday Sweet Sixteen, Calendar Girl and Oh! Carol, a lament for his high school sweetheart, Carole King.
At the Brill Building, Sedaka and Greenfield were joined by other up-and-coming writers and lyricists including Neil Diamond, Paul Simon and King.
"Neil Sedaka was so talented, and he inspired me to follow my dream of being a songwriter," King said on her Facebook page. "With love and gratitude and condolences to his family."
Micky Dolenz of the Monkees also paid tribute to Sedaka, saying on Instagram that he was "one of those rare songwriters who could do it all."
From 1959 to 1962, Sedaka had 10 records in the Top 10, including Calendar Girl, Oh! Carol, Happy Birthday Sweet Sixteen and Next Door to an Angel. But in the mid-1960s, the Brill Building sound, influenced by the doo-wop groups of the New York City streets, was pushed off the charts by the Beatles -led British Invasion and the psychedelic and protest music that followed.
Sedaka would endure 13 years "in the wilderness," as he described it to the AP.
Sedaka was among the lucky, however, enjoying a renaissance that began in the mid-'70s thanks to the patronage of Elton John, whom he met at a party after moving his wife and two kids to England to take advantage of his lingering popularity there. John signed him to his fledgling, US-based Rocket Records label, providing him a chance at more hits with the album Sedaka's Back.
At Rocket, Sedaka and a new writing partner, Philip Cody, topped charts with Bad Blood and the joyous Laughter in the Rain. He also achieved a rare feat with Breaking Up Is Hard to Do. His original up-tempo version went No.1 in 1962. He re-recorded it as a slow ballad in 1975 and that, too, went No.1.
He recorded five albums from 1972 to 1976. They included hits Standing on the Inside, That's Where the Music Takes Me and Our Last Song Together, about his break-up with Greenfield, with whom he began writing songs when Sedaka was only 13 and Greenfield 16.
The Captain & Tennille's cover of his Love Will Keep Us Together was also a chart-topper in 1975.
Sedaka was inducted into the Songwriters Hall of Fame, but the Rock & Roll Hall of Fame eluded him despite a fan petition drive.
Sedaka married wife Leba in 1962. They had two children. Daughter Dara recorded a duet with her father in 1980, Should've Never Let You Go. It was a hit, but she never joined him in the music business. Son Marc is a film and television writer.
