Sanchez is expected to back up starter Mike Glennon for the Bears, who are coming off a 3-13 season and finished last in the NFC North.
The 30-year-old Sanchez, the New York Jets' 2009 first-round pick (fifth overall) out of USC, visited with the Bears on Thursday and now joins his fifth NFL team.
Glennon, who was the backup for the Tampa Bay Buccaneers and hasn't started a game in over two years, was signed by the Bears earlier this month to a three-year deal worth $43.5 million after the team cut quarterback Jay Cutler.
Sanchez is the third quarterback on the Bears roster, joining Glennon and Connor Shaw, who missed the entire 2016 regular season after suffering a broken leg suffered in the team's fourth preseason game.
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The Carolina Panthers signed running back Jonathan Stewart to a one-year contract extension through the 2018 season.
Stewart, who turned 30 on Tuesday, was set to count $8.5 million against the salary cap in 2017, but the new deal reportedly will spread the money out to save cap space.
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Former Minnesota Vikings running back Adrian Peterson is reportedly asking for a premium price on the open market, and teams are not willing to meet the demand.
Peterson remains unsigned during free agency and ESPN's Jeremy Fowler reported that it is because the asking price is too high.
A source from a team in the market for a running back told ESPN that Peterson wanted more than $8 million in the first year of a contract.
Eddie Lacy was one of the first running backs signed in free agency, accepting a one-year deal with the Seattle Seahawks worth up to $5.5 million that includes a weight clause.
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The Indianapolis Colts released defensive tackle Arthur Jones to clear salary-cap space.
Jones, 30, was set to count $7.35 million against the cap in 2017 after the Colts signed him to a five-year, $33 million deal as an unrestricted free agent on March 13, 2014. Indianapolis saves about $5.15 in cap space by releasing Jones, according to ESPN.
Jones received a four-game suspension during the offseason last year for using performance-enhancing drugs.
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The Washington Redskins signed unrestricted free agent wide receiver Brian Quick to add depth at the position.
The Redskins lost starting wide receivers DeSean Jackson (Tampa Bay Buccaneers) and Pierre Garcon (San Francisco 49ers) via free agency.
Quick is the second free agent receiver to sign with the Redskins this month, joining Terrelle Pryor.
Terms of Quick's deal were not disclosed.
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The Dallas Cowboys signed veteran offensive tackle Byron Bell to a one-year contract.
Financial terms of the deal were not disclosed.
Bell missed the entire 2016 season after dislocating his ankle during an offseason practice while with the Tennessee Titans. He started all 16 games for the club in 2015. (Editing by Andrew Both)