The hits created by the pair included Will You Love Me Tomorrow,(You Make Me Feel Like) A Natural Woman, Up on the Roof and The Loco-Motion.
Goffin's wife, Michelle Goffin, confirmed his death at his home in Los Angeles.
Goffin, who married King in 1959, wrote more than 50 top 40 hits, including Pleasant Valley Sunday for the Monkees, Some Kind of Wonderful for the Drifters and Take Good Care of My Baby by Bobby Vee. He was equally at home with humourous lyrics or achingly sad ones, and he did it for solo artists and multiple voices.
Louise Goffin, one of his daughters, said her dad "wore his heart on his sleeve, and I am deeply blessed to have had a father who could so easily make the world laugh and cry with just a spiral notebook and a pen".
King and Goffin divorced in 1968, but Goffin kept writing hits, including Savin' All My Love for You for Whitney Houston. Goffin and King were inducted into the Songwriters Hall of Fame in 1987 and the Rock and Roll Hall of Fame three years later.
King said in a statement that Goffin was her "first love" and had a "profound impact" on her life.
"Gerry was a good man with a dynamic force, whose words and creative influence will resonate for generations to come," King said. "His words expressed what so many people were feeling but didn't know how to say."
The Goffin-King love affair is the subject of the Tony Award-nominated musical Beautiful: The Carole King Musical on Broadway. King, while backing the project and with one of their daughters acting as a producer, had avoided seeing it for months because it dredged up sad memories. She finally sat through it in April.
The musical shows the two composing their songs -- and competing against the formidable rival team of Barry Mann and Cynthia Weil -- at Aldon Music, the Brill Building publishing company in Manhattan that also employed Neil Sedaka, Howard Greenfield and Carole Bayer Sager.
The show ends just as King is enjoying fame for her groundbreaking solo album Tapestry. Though it also alleges Goffin's womanising and mental instability were causes of the breakup, he happily attended the opening of the musical.
Goffin was born in Brooklyn in 1939 and was working as an assistant chemist when he met King at Queens College.
"She was interested in writing rock 'n' roll, and I was interested in writing this Broadway play," Goffin told Vanity Fair in 2001. "So we had an agreement where she would write [music] to the play if I would write [lyrics] to some of her rock 'n' roll melodies.
"And eventually it came to be a boy-and-girl relationship. Eventually I began to lose heart in my play, and we stuck to writing rock 'n' roll."
A whirlwind romance led to a marriage and their first hit, when King was only 17 and Goffin was 20, Will You Love Me Tomorrow for the Shirelles, which a pregnant King helped write while suffering morning sickness.
Goffin is survived by his five children and his wife.