Edwards joined the Motown group in 1968 and stayed until 1976, during which time the band notched up hits such as Papa Was a Rollin’ Stone and Ball of Confusion.
His cause of death has not yet been revealed.
“He was an amazing performer and singer and the whole Temptations family are grieving at his sad passing,” the group’s agent said.
The Alabama-born singer joined the group when they fired David Ruffin and his gritty vocals helped propel the group to greater chart success.
He left the group after they split with Motown Records in the late 1970s, returning again for several stints in the 1980s.
In the 1990s he toured with a splinter group, but could not use the Temptations name after two members went to court for an injunction.
Edward died in a Chicago hospital just a day before his 75th birthday.
There are unconfirmed reports in US media that he may have died following complications related to meningitis, which he reportedly first fell ill with last spring.
A post on the Temptations Facebook page on 30 January urged fans to send their prayers to the singer and his family.
Motown great Martha Reeves told the Detroit Free Press: “My heart is very heavy. I feel like I’ve been hit by a sledgehammer.”
Nineties rap star MC Hammer tweeted: “R.I.P. Dennis Edwards one of my favorites in the industry. Good Soul Great Artist !!!!”
More from Entertainment
It’s official! Spice Girls confirm reunion to work on unconfirmed projects
Comedian Amy Schumer says she was ‘flat-out raped’ as a teenager
Craig McLachlan sues ex-Rocky Horror Show co-star over sexual harassment claims
‘My mom tried to check out’: Dwayne ‘The Rock’ Johnson opens up about his mother’s suicide attempt
Jim Carrey cleared of role in suicide of ex-girlfriend Cathriona White
Actor Robert Wagner ‘person of interest’ over wife Natalie Wood’s death, police say
Reverend Jesse Jackson also tweeted, saying: “Dennis Edwards, former lead, singer of the #Temptations. I went to visit him at @RushMedical. He slept away.
“In his life he inspired millions around the world. We shall all remember him. So talented. He is above #CloudNine, going higher. RIP my brother beloved.”