Over the course of her career, Norman won four Grammys for her recordings and one for lifetime achievement, for which she was also given a National Medal of Arts.
She was one of the first African-Americans to break through into the world of opera and became known for her performances of works by Richard Wagner.
The New York Met, with whom she sang more than 80 performances, called Norman "one of the great sopranos of the past half-century" in a statement on her death.
"Jessye Norman was one of the greatest artists to ever sing on our stage," said Met General Manager Peter Gelb. "Her legacy shall forever live on."
Her broad repertoire, which also included jazz performances, featured works from Francis Poulenc, Leos Janacek, Bela Bartok, Giuseppe Verdi, Richard Strauss and Arnold Schoenberg, among others.
Norman's brother and sister, James Norman and Elaine Sturkey, released a statement paying tribute to her and her musical achievements, quoted by NPR.
"We are equally proud of her humanitarian endeavors addressing matters such as hunger, homelessness, youth development, and arts and culture education," they said.
The cause of death was reported as septic shock and multi-organ failure secondary to complications of a spinal cord injury she had sustained in 2015.
Born on September 15, 1945, Norman was one of five children born into a musical family in Augusta, Georgia.
She studied music in Washington and later won the Munich International Music Competition in 1968, before celebrating her opera debut at the Deutsche Oper in Berlin as Elisabeth in Wagner's "Tannhaeuser."
News of her death prompted an outpouring of tributes.
"What a stunning, saddening loss today," US opera star Renee Fleming wrote on Twitter.
"The world has lost one of the greatest voices that we have ever had and heard. She poured herself out for us. Rest in peace, dearest Jessye Norman," singer and composer Rufus Wainwright said.
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