Bortles will operate as a backup behind Jared Goff, who guided the Rams to Super Bowl LIII last season. He'll also work under head coach Sean McVay, who helped turn Goff into a successful quarterback after he struggled mightily as a rookie under Jeff Fisher.
"I mean, I think as a quarterback, there's not really anybody else you'd rather be around if you had your pick," Bortles said of his new coach, according to the team's website. "What he's done, the people that have been taken out of here for head coaching jobs and OC jobs in other places, I think is a testament to how good he is at what he does, how good of a teacher and a coach he is.
"And you watch them play, and the effort and intensity that they play at speaks to the type of head coach he is and how he gets the guys going."
The 26-year-old was released by the Jaguars after five seasons. Jacksonville drafted him third overall in 2014.
In 13 games last season, Bortles threw for 2,718 yards with 13 touchdowns and 11 interceptions, and he was benched in favor of Cody Kessler late in the campaign.