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Edwards died at a hospital in Chicago on Thursday night or Friday morning of complications from an unspecified illness, his manager Toby Ludwig said by phone.
The singer, who lived outside St. Louis, would have celebrated his 75th birthday on Saturday.
The Alabama-born Edwards replaced David Ruffin as lead singer of The Temptations in 1968.
Edwards sang lead on some of the vocal group's most memorable hits, including Papa Was a Rollin' Stone, a 1972 release that earned Edwards and the group two Grammy Awards, and I Can't Get Next To You, which topped the pop charts in 1969.
Edwards left The Temptations around the time the group left Motown to sign with Atlantic Records in 1977. He rejoined and left multiple times in the 1980s, when the group enjoyed far less success on the pop charts than in the previous two decades.
Edwards was inducted into the Rock and Roll Hall of Fame in 1989 as a member of The Temptations.