The 26-year-old quarterback has been brought in as a back-up to Jared Goff.
Bortles visited the Rams on Monday and a deal was hashed out between the two parties.
Despite his young age Bortles is an experienced quarterback, having spent five years as the starting quarterback for the Jacksonville Jaguars.
However, the former No 3 overall pick of the 2014 NFL Draft was deemed to be surplus to requirements only hours after the Jaguars announced their acquisition of Super Bowl MVP and former Philadelphia Eagles quarterback Nick Foles.
The Rams needed a new back-up quarterback with Sean Mannion going into free agency and they have decided to go with Bortles.
Mannion, a third-round pick in 2015, spent the past four seasons as a back-up with the Rams.
Rams coach Sean McVay elected to use Mannion in the majority of their snaps for the 2018 pre-season, but he struggled to make an impact, which caused concern for the coaching staff if he was ever needed to fill in for Goff.
Whereas Bortles, although plagued by inconsistency throughout his career, will bring experience to the back-up position.
Last season Bortles threw for 2,718 yards, 13 touchdowns and 11 interceptions for the Jaguars and had a passer rating of 79.8.
The Central Florida graduate also posted a career-high passing completion percentage of 60.3.
In comparison Goff threw for 4,688 yards, 32 touchdowns and 12 interceptions and had a passer rating of 101.1 – he also posted a career-high passing completion percentage of 64.9.
The Jaguars cutting Bortles was not an unexpected move, especially after the organisation benched the player for Cody Kessler after he put in poor displays in losses to the Buffalo Bills and the Pittsburgh Steelers.
Against the Steelers he threw for a total of 104 yards and was sacked six times and the following week against the Bills he threw for 127 yards, one touchdown and two interceptions, while posting a passer rating of 46.8.
McVay isn’t bringing in Bortles to compete with Goff for the starting position, but he knows the experience will be beneficial as their No 2.
Over the course of his career Bortles has played in 75 games in the NFL, completing 59.3 per-cent of his passes for a total of 17,646 yards.
He also has 103 touchdowns and an 80.6 career passer rating.
Bortles is one of only 15 quarterbacks to surpass 100 touchdown passes since he entered the league in 2014.
However he also leads all quarterbacks in interceptions, with 75, and all players in turnovers, with 94, during the same period.