Turner had coached the team since 2007. Smith had been with the organization twice, most recently since 2001, and had been general manager since April 2003.
San Diego won a total of 32 games and made three playoff appearances over Turner's first three seasons as coach but had 24 wins in the last three years without returning to the playoffs.
That includes a 7-9 record this year, after three wins in the Chargers' last four games.
"I thank A.J. and Norv for the determination and integrity they brought to the Chargers each and every day," said Chargers President Dean Spanos. "Both Norv and A.J. are consummate NFL professionals and they understand that in this league, the bottom-line is winning.
"My only goal is the Super Bowl, and that is why I have decided to move in a new direction with both our head coach and general manager positions."
The Chargers said they hired former Green Bay General Manager Ron Wolf as a consultant in the search for replacements in the two key posts.