Cobb County investigators say the 29-year-old Oliver was found dead Tuesday night at his home in Marietta, about 20 miles northwest of downtown Atlanta.
Police said Wednesday that Oliver died of a self-inflicted gunshot wound.
Chargers reserve safety Darrell Stuckey, who played with Oliver for two seasons, was stunned by the news.
"For me it's a shock because where he was when he was with us, there's no way you can imagine that happening," Stuckey said. "So just you never know. It's never a good time or a good reason, and I just send my prayers out to him and his family."
The Chargers offered condolences to the Oliver family in a prepared statement.
"Everyone in the Chargers family is sad today after hearing the news about Paul," the 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 played for the Chargers from 2007 to 2011. His best season was 2010, when he started eight times and had 62 tackles.
"He was a good guy," Stuckey said. "He was a great player. He played with a lot of passion. He loved to get around the ball, try to get a hand on the ball and get it out at all times. He was a guy that played with a lot of energy when he was on the field, and he wanted to get on the field however he could, and would do whatever it took."
Oliver was a 2007 fourth-round supplemental draft pick out of Georgia after he was ruled academically ineligible his senior year.
Oliver was released by the New Orleans Saints after training camp in 2011, and returned to San Diego that season.
Information from ESPN.com Chargers reporter Eric Williams and The Associated Press was used in this report.