His death marks the latest in a string of suicides among former professional football players.
"Everyone in the Chargers family is sad today after hearing the news about Paul," a statement from the NFL team said. "He was part of our family for five years. At just 29 years old, he still had a lifetime in front of him. Right now all of our thoughts and prayers are with his family during this most difficult time."
Oliver leaves behind a wife and two children, The Atlanta Journal-Constitution reported.
"We appreciate all the thoughts and prayers," Oliver's family said in a statement to The San Diego Union-Tribune. "We request privacy in the wake of this tragic loss."
Mark Richt, coach of the University of Georgia Bulldogs, called it "a very sad day."
"I just want to say it's been rough," he told reporters. "I just want to tell everybody in his family that we're thinking about them and we love them. We'll do whatever we can to help."
Police found Oliver's body Tuesday night at the bottom of a set of stairs in a home in Marietta, Georgia, Cobb County police spokesman Sgt. Dana Pierce said. A family member had called 911.
The county medical examiner ruled the death a suicide by handgun and gave police authorization to release the cause.
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Oliver played for the Chargers from 2007 to 2011, recording 144 tackles in 57 games.
A former teammate, Eric Weddle, described Oliver as "charismatic, funny but also quiet and reserved," The Union-Tribune reported. "He never said a bad word about anyone. Just a good, genuine guy."
Oliver's high school coach in Georgia, Bruce Cobleigh, said Oliver was a leader.
"This is a real tough situation for everybody because this isn't Paul," Cobleigh told CNN's Brooke Baldwin. "This is surprising, shocking. He was really outgoing. He was really well-liked, a leader, hard, hard worker.'
Cobleigh said he hadn't talked with his former player in recent years as much as when he was in Georgia, but the coach had fielded calls much of Wednesday from former teammates of Oliver who were all surprised by his death.
The circumstances of his apparent suicide were not immediately clear.