Sanchez, who visited the Bears on Thursday, provides additional depth behind starter Mike Glennon.
The Bears prioritized finding another proven backup to work alongside Glennon, who hasn't started a game in over two years. The only other quarterback on Chicago's depth chart is Connor Shaw, who missed the entire 2016 regular season because of a broken leg he suffered in the team's fourth exhibition game. Prior to joining the Bears, Shaw played in just one regular-season game for the Cleveland Browns in 2014.
The Bears are still expected to strongly consider selecting a quarterback in the upcoming draft.
Sanchez, the fifth overall pick in the 2009 draft, found himself with the Dallas Cowboys in 2016 after he was unable to win the Denver Broncos' starting job in a battle with Trevor Siemian and was released. The Cowboys were in need of a quarterback after Tony Romo and Kellen Moore were out with injuries.
The 30-year-old Sanchez saw action in two games for Dallas, completing 10 of 18 passes for 85 yards and two interceptions. He also forged a strong relationship with rookie Dak Prescott, with Sanchez having gone through many of the same experiences while directing the New York Jets to the AFC title game in each of his first two NFL seasons.
After his five-year run with the Jets ended in 2013, he spent the next two seasons with the Eagles, starting 10 games.
He has a 37-35 career record with 86 touchdown passes and 86 interceptions to go along with 15,219 passing yards.
ESPN's Todd Archer contributed to this report.