Per NFL Network's Mike Garafolo, the Jaguars and Glennon agreed to terms Friday.
The Jaguars have been linked to some veteran quarterbacks at points this offseason after trading Nick Foles to the Chicago Bears in March.
General manager David Caldwell told Mike Florio on the #PFTPM podcast earlier this week that they had "some discussions" with Andy Dalton and his agent before Dalton signed with the Dallas Cowboys.
Head coach Doug Marrone said on the May 1 episode of Good Morning Football (h/t NFL Network's Ian Rapoport) that even though Minshew is "no doubt" Jacksonville's starter, the team was still looking to make upgrades.
"We’re still looking to make sure we're upgraded at each position," Marrone said. "There are some veterans out there that we might look at to bring in, along with the young guys we have."
Glennon spent last season with the Oakland Raiders. He only appeared in two games, completing six of 10 passes for 56 yards and one touchdown.
In seven seasons with four different teams, Glennon has a 6-16 record in 22 career starts. The 30-year-old has thrown for 5,163 yards, 36 touchdowns, 20 interceptions and a 60.9 completion percentage in 29 games.