According to NFL Network's Ian Rapoport, the deal is worth $2.25 million.
Woods, 25, spent the first four years of his NFL career with the Dallas Cowboys after they selected him in the sixth round of the 2017 NFL draft out of Louisiana Tech.
After spending his rookie year primarily as a backup, Woods was a full-time starter for the Cowboys in each of the next three seasons, starting all 44 games he appeared in.
In 60 career NFL regular-season games, Woods has 247 tackles, five interceptions, 18 passes defended, three forced fumbles and two fumble recoveries.
He recorded two interceptions each in 2018 and 2019, while finished with a career-high 77 tackles during the 2019 campaign as well.
Woods finished without an interception last season for the first time, but he still racked up 72 tackles and one pass breakup.
The Vikings have been hard at work reshaping their secondary this offseason, as they signed three-time All-Pro cornerback Patrick Peterson and reportedly agreed to a deal with corner Mackensie Alexander on Saturday, per Rapoport.
Safety was still a need for the Vikings after Anthony Harris signed with the Philadelphia Eagles, and they addressed it with Woods.
He is in good position to start next season alongside Harrison Smith, with Peterson, Alexander, Jeff Gladney, Cameron Dantzler and Mike Hughes providing plenty of depth at the corner spots.
Minnesota ranked just 25th in the NFL against the pass last season and 29th in scoring defense, but the Vikes should fare much better in 2021 given their free-agent signings.
Mike Zimmer is a defensive-minded head coach, and he figures to make the most of the talent general manager Rick Spielman has brought in this offseason.