The deal is worth $62.5 million with $17 million fully guaranteed at signing, a source told ESPN's Dan Graziano.
The move fills a huge void for the Chargers. Dan Feeney had moved to center last season from guard after Mike Pouncey went on injured reserve in September with a hip injury. Pouncey retired this offseason.
The Steelers' starting right tackle for the 2018 and 2019 seasons, Feiler moved to left guard for the 2020 season after the departure of Ramon Foster forced the line to reshuffle. He started 13 games, going on the injured reserve list with a pectoral injury before returning for the first-round playoff loss against the Cleveland Browns.
The 28-year-old Feiler played every single offensive snap of the 2019 season and 86% of snaps in 2020 after signing a restricted free-agent tender in April 2020.
The Chargers also announced Monday that they had agreed to a multiyear deal to re-sign cornerback Michael Davis, who appeared in all 16 games last season, making 14 starts and finishing with three interceptions.
Linsley earned first-team All-Pro honors for this past season, becoming the first Green Bay Packers center to do so since Jim Ringo in 1963.
He started 13 games, missing three because of a knee injury but returning in time for the playoffs. He helped the Packers tie for second in the NFL for fewest sacks allowed and was part of the top-scoring offense in the NFL.
The 2014 fifth-round pick from Ohio State became an immediate starter as a rookie and has 99 regular-season season starts dating to that 2014 season. He had a stretch from late in the 2016 season to early in the 2019 season in which he was on the field for more than 2,700 straight offensive snaps.
Linsley, 29, signed a three-year, $25.5 million contract extension with Green Bay late in the 2017 season.
He was one of two offensive line starters for the Packers who entered the 2020 season in the final year of his contract. The team signed All-Pro left tackle David Bakhtiari to a four-year, $103.5 million extension in November. Bakhtiari tore his ACL in practice on Dec. 31 and might not be ready for the start of the regular season.
ESPN's Shelley Smith, Rob Demovsky and Brooke Pryor contributed to this report.