Chargers coach Anthony Lynn had said a point of emphasis this offseason would be finding a consistent kicker who can stick around long term.
The Bolts used five kickers in 2017 -- including punter Drew Kaser -- and finished at a league-low 67 percent on field goal attempts.
At an end-of-season news conference, general manager Tom Telesco took blame for the team's struggles at the position, saying he didn't do a good enough job addressing the position.
In January, former Tampa Bay Buccaneers kicker Roberto Aguayo signed a reserve/future contract with the team. Nick Rose is also under contract after the Chargers claimed him off waivers when the Washington Redskins released him in Week 16.
Sturgis, 28, suffered a hip flexor injury in the 2017 season opener for the Philadelphia Eagles and was placed on injured reserve, and the team signed rookie Jake Elliott off the Cincinnati Bengals' practice squad.
Elliott secured the job with his big leg, nailing a 61-yard game-winning field goal at the end of regulation against the New York Giants in Week 3. He went on to hit 5-of-6 from 50-plus yards during the Eagles' Super Bowl run.
Sturgis spent two seasons with the Miami Dolphins before joining the Eagles in 2015. He has connected on 81 percent of his field goal tries over four-plus seasons and is 13-of-24 from 50-plus yards.
ESPN's Eric D. Williams and Tim McManus contributed to this report.