The Redskins did not disclose terms of the deal, but a source told ESPN's Adam Schefter the contract is for one year and worth $4 million.
The Redskins plan to use Flowers, a former first-round pick and starting tackle, as Shawn Lauvao's replacement at left guard.
Flowers, who visited the facility Monday, will also be used at tackle as second-year Geron Christian recovers from a torn MCL suffered during the season.
The Redskins need depth and a lot of options inside, especially at left guard. The Redskins went through numerous players at left guard last year because of injuries. They might draft one next month, but they needed healthy options and like Flowers' physical play and athleticism.
Flowers, 24, was the ninth overall pick in 2015 by the New York Giants but never played at the high level expected of a top-10 pick.
He started at left tackle in 49 of the 52 games in which he played for the Giants from 2015 to '18 but lost his starting job last season in Week 3 to Chad Wheeler, who signed with the Giants as an undrafted free agent in 2017.
The Giants cut Flowers on Oct. 10, and the Jaguars signed him two days later to a one-year contract worth $705,000. A rash of injuries along the offensive line forced him into the starting lineup, and he started the final seven games of the season.
ESPN's John Keim and Michael DiRocco contributed to this report.