He will provide depth after starter Drew Lock suffered a rotator cuff strain in Week 2. ESPN's Adam Schefter reported he will be out two to six weeks.
Jeff Driskel is the only other healthy quarterback on the roster and is expected to start in Week 3 against the Tampa Bay Buccaneers.
"It's Jeff's [job] right now," head coach Vic Fangio said. "That's the way we're proceeding and anticipating going right now."
Bortles, 28, spent the first five seasons of his career as the starting quarterback for the Jacksonville Jaguars, throwing for 17,646 yards, 103 touchdowns and 75 interceptions while completing 59.3 percent of his passes. He also rushed for 281 yards and eight scores.
And while he led the Jaguars to the AFC Championship Game in the 2017 postseason, his tenure in Jacksonville was rocky, as the team was just 24-49 on his watch.
The Jaguars cut him in March 2019 after signing Nick Foles—who has since been traded to the Chicago Bears—and Bortles joined the Los Angeles Rams as Jared Goff's backup. He threw just two passes last season.
His history as a starter made him an intriguing target for teams seeking a quality backup, or even a short-term starter. Barring a major turnaround, however, Bortles' days as a franchise signall-caller seem over.
But the Broncos will be happy to add solid depth to their quarterback room.