Glennon, 28, spent four seasons with the Tampa Bay Buccaneers, mostly as a backup, before signing a three-year, $45 million contract with Chicago a year ago. His stint as the Bears' starter lasted just four games before he was replaced by rookie Mitchell Trubisky. Glennon didn't play the rest of the season.
Quarterback Sam Bradford also intends to sign with the Cardinals, a source told ESPN's Adam Schefter. Bradford's deal is expected to be for one year and $20 million, including $15 million guaranteed, with a one-year option for $20 million, according to the source.
The NFL Network first reported Glennon's deal moments after the Bears announced he had been released.
Before he was released, Glennon was scheduled to make $12.5 million as Trubisky's backup in 2018. The Bears were already on the hook for Glennon's fully guaranteed $2.5 million roster bonus, putting the total price tag for his one-year stint in Chicago at $18.5 million.
Glennon turned the ball over eight times -- five interceptions and three fumbles -- in four starts before Chicago made the switch in Week 5 to Trubisky, the second overall pick in the 2017 NFL draft.
Glennon started 18 games for the Buccaneers from 2013 to 2014. He has thrown for 4,933 career yards and has 34 touchdowns and 20 interceptions. He also has seven career fumbles.
ESPN's Jeff Dickerson contributed to this report.