Police said Oliver, 29, shot himself Tuesday evening, U-T San Diego reported.
The police report said Oliver's wife, Chelsea, and two children witnessed his death.
Oliver was drafted by San Diego after being declared academically ineligible at the University of Georgia, The Atlanta Journal-Constitution said. He was a star for three years at the university and during his high school career at Harrison High School in Kennesaw, Ga.
"Everyone in the Chargers family is sad today after hearing the news about Paul," the Chargers said in a statement. "He was part of our family for five years."
Eric Weddle, a Chargers Safety, told U-T San Diego his former teammate was both quiet and funny.
"He never said a bad word about anyone. Just a good genuine guy," Weddle said. "From the moment he got here, he was up front. Loved the game. You could always count on him. Every year, it seemed like he was a backup who could play special teams. Then he got into games, and he always played well."