Fuqua was born in Louisville, Kentucky, United States. He was the nephew of Charlie Fuqua of the Ink Spots. In 1951, with Bobby Lester, Alexander Graves and Prentiss Barnes, he formed a vocal group, the Crazy Sounds, in Louisville, later moving with other members of the group to Cleveland, Ohio. There they were taken under the wing of disc jockey Alan Freed, who renamed them the Moonglows, after his own nickname, Moondog”. The Moonglows’ first releases were for Freed’s Champagne label in 1953. They then recorded for the Chance label in Chicago, before signing with Chess Records in 1954. Their single “Sincerely” reached number 1 on the Billboard R&B chart and number 20 on the Hot 100 in late 1954.

Recording for Chess Records, Fuqua initially shared lead vocals with Lester but eventually asserted himself as the leader of the group. This changed in 1957 when he, in effect, fired the other members and installed a new group, previously known as the Marquees, which included Marvin Gaye. The new group, billed as Harvey and the Moonglows, had immediate success with “Ten Commandments of Love” (number 22 on the Billboard Hot 100). Fuqua left the group in 1958.

Fuqua left the Moonglows when Leonard Chess suggested that he join Anna Records in Detroit. At Anna Records, Fuqua began working with Anna Gordy, Billy Davis, Lamont Dozier and Johnny Bristol. He also introduced Marvin Gaye to Anna’s brother, Berry Gordy, and married their sister Gwen Gordy. In 1961, he started his own labels, Tri-Phi Records and Harvey Records, whose acts included the Spinners, Junior Walker and Shorty Long. However, tiring of running a small independent label, Fuqua welcomed the opportunity to work at Motown; he was hired to head the label’s Artist Development department and also worked as a producer for the company. Fuqua brought the Spinners and Johnny Bristol to Motown and co-produced several hits for Bristol. He was also responsible for bringing Tammi Terrell to the label and for suggesting and producing her duets with Marvin Gaye, including “Ain’t No Mountain High Enough” and “Your Precious Love”. In 1962, with the Five Quails, Fuqua had a minor hit with “Been a Long Time”.

Around 1971, Fuqua left Motown and obtained a production deal with RCA Records, for which he had particular success with the band New Birth. He also discovered the disco pioneer Sylvester and “Two Tons o’ Fun” (also known as the Weather Girls), producing Sylvester’s hit singles “Dance (Disco Heat)” and “You Make Me Feel (Mighty Real)” in 1978 and his album Stars in 1979. He also served as Smokey Robinson’s road manager. In 1982, he reunited with Marvin Gaye to produce the singer’s Midnight Love album, which included the single “Sexual Healing”. In 2000, he set up his own record company, Resurging Artist Records. He served as a trustee of the Rhythm and Blues Foundation. Fuqua co-wrote one of the most famous disco instrumentals, “K-Jee”, recorded originally by The Nite-liters, from which New Birth was an offshoot band, and then Philadelphia session musicians MFSB for the movie Saturday Night Fever.

The Moonglows reunited temporarily in 1972. They were inducted into the Rock and Roll Hall of Fame in 2000.

In November 1982, disco star Sylvester filed a lawsuit against Fuqua and Fantasy Records, which led to a judgment that the company had been withholding money from him, in the amount of $218,112.50. Fuqua was unable to pay more than $20,000, so that Sylvester never received most of the money that was legally owed to him.

In March 1995, Fuqua and with his wife, Carolyne, incorporated the Foundation for the S.T.A.R.S., a nonprofit organization that reaches out to address some of the difficulties to underprivileged youth in the inner cities of America, with the belief that every dream should have the opportunity to be realized.

Fuqua resided in Las Vegas, Nevada, until his death from a heart attack in a hospital in Detroit on July 6, 2010.

On June 25, 2019, The New York Times Magazine listed Harvey Fuqua among hundreds of artists whose material was reportedly destroyed in the 2008 Universal fire.