A statement released on behalf of his wife, Claybra Selmon, said he died at a Tampa hospital surrounded by family members.
"For all his accomplishments on and off the field, to us Lee Roy was the rock of our family. This has been a sudden and shocking event and we are devastated by this unexpected loss," the statement said.
Selmon was hospitalized Friday, and the Buccaneers confirmed later that he suffered a stroke.
The Glazer family, which owns the team, released a statement mourning him.
"Tampa Bay has lost another giant. This is an incredibly somber day for Buccaneer fans, Sooner fans, and all football fans. Lee Roy's standing as the first Buc in the Hall of Fame surely distinguished him, but his stature off the field as the consummate gentleman put him in another stratosphere," the statement said.
Selmon and his brother, Dewey, were both chosen as All-Americans in 1975 when the Sooners won their second straight championship under Barry Switzer. They followed older brother Lucious to Oklahoma, and the three played together during the 1973 season.
Selmon followed his Hall of Fame college career with an equally impressive run in the NFL. He was the No. 1 pick in the 1976 draft - the first ever selection by expansion Tampa Bay - and suffered through a winless inaugural season before achieving success. In 1979, he won the NFL Defensive Player of the Year award when he helped Tampa Bay make it to the NFC championship game. The Buccaneers also won the NFC Central title two years later.
Selmon was inducted into the Pro Football Hall of Fame in 1995. Presented by brother Dewey, Lee Roy said it was his family background that was noteworthy and not his accomplishments on the field.
"People have said, 'Your parents must be proud of you,' but I'm more proud of them," he said.
Selmon played a key role in the creation of the football program at South Florida, where he was the associate athletic director starting in 1993 and served as the AD from May 2001 until he stepped down in February 2004 because of health concerns.
While accompanying the South Florida football team to a game against Oklahoma in 2002, Lee Roy Selmon said he was humbled that Switzer had called him his greatest player.
"I see myself as just having been a teammate with so many great players and coaches," he told The Associated Press. "I'm floored by such a generous compliment."
Lee Roy Selmon was born Oct. 20, 1954, in Eufaula, Okla., to Jessie and Lucious Selmon Sr. and raised on a farm with eight siblings. The three who'd go on to star for the Sooners could have ended up at Colorado, if not for a last-minute recruiting.
Larry Lacewell described in the book "Wish Bone" that the Sooners didn't decide to recruit Lucious Selmon until Barry Price switched his commitment from Oklahoma to Oklahoma State the day before signing day. Lacewell showed up at the Selmons house to find Colorado coach Eddie Crowder there. When he got his chance to talk to the family, he stayed at the house until the two younger brothers had fallen asleep and he had convinced the Selmon parents it was better for Lucious to play 100 miles away than 600.
It ended up being a key day for the program.
Oklahoma went 10-0-1 with all three Selmon brothers playing together in 1973, then won national title the next two seasons. Lee Roy Selmon won the Lombardi Award and the Outland Trophy in 1975. He ended his college career with 335 tackles, a school record for a linemen at the time, and 40 for a loss.
He went on to record 78½ sacks and earn six consecutive Pro Bowl selections during his nine-year career. He retired after the 1984 season.