Greenwood County coroner James T. Coursey told ESPN that Adams, a Greenwood native, was taken to the emergency room at Self Regional Hospital, where he was pronounced dead at 9 a.m.
Adams, who had just completed his third season in the NFL, went into cardiac arrest at his family's home early Sunday morning, said Marcia Kelley-Clark, chief deputy coroner for Greenwood County.
The autopsy showed Adams had an enlarged heart, a condition Kelley-Clark said can often lead to a heart attack. But Adams' relatives didn't know about it.
"Nobody was aware of any kind of medical condition," Kelley-Clark said.
Toxicology tests are being run by the State Law Enforcement Division, though drug use was not suspected as a factor in Adams' death. However, those results probably will not be available for at least two months, Kelley-Clark said.
"I remember him at the 2007 draft as a fine young man," NFL commissioner Roger Goodell said of Adams on Sunday. "Our condolences to Gaines' family, his teammates on the Bears and Buccaneers, and their organizations on their loss."
In 47 games over three seasons with the Bears and the Tampa Bay Buccaneers, Adams had 67 tackles, including 13.5 sacks.
"We are stunned and saddened by the news of Gaines' passing," the Bears said in a statement. "Our prayers are with his family during this difficult time."
Adams was selected fourth overall in the 2007 NFL draft by Tampa Bay, but was unable to live up to expectations that he would revive the Buccaneers' once-feared pass rush. He fell short of the benchmark set by Buccaneers coach Raheem Morris, who said at the start of training camp that Adams would be considered a "bust" if he didn't reach double digits in sacks. He was traded to Chicago in October for a second-round pick in the 2010 draft.
Adams said during training camp that he welcomed the challenge posed by Morris, who also called out the third-year pro after Adams began the season with lackluster performances in the first three games.
"In football you need that. Players tend to get in their own element and do things that they want to do. They need to be called out sometimes. He's the coach. Whatever he says, goes," Adams said in early August.
On Sunday, Morris called Adams "a true team player and a positive influence to everyone he met. My prayers go out to his family."
The Bucs' ownership and front office and Adams' former Tampa teammates were saddened by his death.
"Gaines was a quiet, humble kid and is far too young to be gone," cornerback Ronde Barber said. "He had so much potential that had yet to be achieved and I am very sad that the full extent of his life won't be realized."
"I still don't want to believe that it is true," added defensive tackle Chris Hovan. "I am deeply saddened that we have lost someone who I considered a friend for life. When he came to Tampa, I took Gaines under my wing; I considered him my little brother and that's how I will always remember him. This is all so unreal and it hasn't really hit me yet."
"Today is a tragic day," said ESPN analyst Jon Gruden, who drafted Adams as the Buccaneers' coach. "Gaines was an impressive kid with such a tremendous future in front of him. He was a great teammate and well-liked by our coaches and all those who had the opportunity to be around him in Tampa."
Adams played brief stints on defense after his trade to the Bears, making five tackles.
Bears linebacker Brian Urlacher told the Chicago Tribune that Adams' death was "crazy."
"I didn't know him that well because he came in during the middle of the season," Urlacher said. "But I did know him. I still saw him every day when I went into work. It's just weird.
"I had a teammate die when I was in college. You just don't know how to handle it. It's just sad, man. It's a bad deal."
Adams was well-known among Clemson fans for breaking up Wake Forest's field goal try and returning it for a touchdown in 2006 to defeat the Demon Deacons.
Tommy Bowden, who was Adams' head coach at Clemson, said he couldn't believe the young player was gone.
"I just couldn't believe it was Gaines," Bowden said. "I will always remember the smile he had on his face and I will always remember his patience."
Information from The Associated Press was used in this story.