The New York Giants and Cincinnati Bengals also put in claims for Mettenberger, a league source told ESPN's Field Yates. The Chargers had priority, however, as they finished 4-12 last season. The Giants finished 6-10, and the Bengals were 12-4.
The Chargers have no clear No. 3 quarterback after Philip Rivers and veteran backup Kellen Clemens. Developmental signal-callers Bryn Renner and Mike Bercovici had been competing for the No. 3 job. Renner was waived to make room for Mettenberger on the roster.
Mettenberger, 24, also knows Rivers from his time at LSU, where the San Diego quarterback's younger brother Stephen began his college career.
At 6-foot-5 and 225 pounds, Mettenberger fits the profile that San Diego looks for in a quarterback, a strong-armed thrower who can make plays inside the pocket.
A sixth-round pick by the Titans in 2014, Mettenberger started 10 games over two seasons. The Titans didn't win any of those games.
Titans general manager Jon Robinson said Wednesday that the team attempted to trade Mettenberger during the NFL draft last month.
"There were a lot of teams we touched base with over the course of the draft weekend that had interest in Zach, and a lot of those teams ended up selecting quarterbacks at some point in the draft,'' Robinson told TitansOnline.com. "For whatever reason those discussions never really manifested or culminated into anything."
Mettenberger completed 60.3 percent of his passes with 12 touchdowns, 14 interceptions and a 75.4 passer rating for the Titans. He had the lowest Total QBR in the NFL since 2015, according to ESPN Stats & Information.
ESPN's Adam Schefter, Eric D. Williams and Paul Kuharsky contributed to this report.