The deal includes $25 million guaranteed, the source said. The Chargers released offensive tackle D.J. Fluker earlier this week.
Okung, 29, played in all 16 games for the Denver Broncos in 2016, a first in his seven NFL seasons. However, he finished tied for the Broncos' team lead in penalties with 11.
Okung, who had shoulder surgery just before the Broncos signed him last year, bet on himself in the contract he largely negotiated on his own. Although announced as a five-year deal, it was essentially a one-year deal with a four-year option.
He was the object of cornerback Aqib Talib's ire after a 16-3 loss to the New England Patriots in Week 15. Talib objected when Okung rose to speak after then-coach Gary Kubiak asked whether anyone wanted to address the team after the game. That started a shouting match between defensive players who had held Tom Brady in check and the offensive linemen, who had taken the brunt of the blame for Denver's dive.
A first-round draft pick (sixth overall) by the Seattle Seahawks in 2010, he played six seasons with Seattle and was a part of the 2013 championship team. He received his only Pro Bowl selection in 2012.
ESPN's Jeff Legwold and The Associated Press contributed to this report.