"I'm just done," Shelmon said. "You know when it's time. It's time for me to go and do some other things with my life."
Shelmon wasn't available for further comment, and Turner didn't return a call seeking comment.
Shelmon coached football for a combined 37 years.
The Chargers fired defensive coordinator Greg Manusky on Thursday and replaced him with linebackers coach John Pagano.
"Clarence was a big part of five AFC West championship teams and three playoff wins in San Diego," Turner said, according to the team's website. "His work ethic and dedication to this team go back a long time, and he's had a positive effect on the many players he coached during his tenure here."
"We changed the culture here," Shelmon said. "(In 2000), the Chargers were 1-15. We went 8-8 and just missed the playoffs my first year in 2002. From that time on, I've seen the team get better and better.
"We've done it both ways. I primarily made my name as being a good running coach and developing backs. We were able to be one of the better teams running the ball. Then when Norv came in, we went to the AFC championship and added more to the passing game, yet we've been able to run the ball fairly well. We bridged the two philosophies, I think, quite well. I'm proud of the small part I've played in it."
The Associated Press contributed to this report.