Terms were not disclosed but a source confirmed to ESPN on Saturday that it's a one-year, $2.25 million deal that includes $1.75 million guaranteed.
The 25-year-old Woods, who developed into a versatile safety with the ability to cover the slot over his first four seasons with the Dallas Cowboys, is expected to fill the Vikings' opening at free safety opposite Harrison Smith after Anthony Harris' departure in free agency.
After finishing the season ranked 29th in points allowed and 27th in yards allowed, Minnesota has focused its efforts on the defensive side. In addition to Woods, the Vikings have acquired only defensive players in free agency -- defensive tackle Dalvin Tomlinson, linebacker Nick Vigil and cornerbacks Patrick Peterson and Mackensie Alexander.
A sixth-round draft pick in 2017, Woods became a full-time starter in his second season with the Cowboys and started his last 44 games, missing four games over three seasons because of injury.
Heading into 2020, he was viewed as a cornerstone piece to the Cowboys' secondary, but he struggled despite finishing second on the team with 72 tackles. He had just two tackles for loss, did not record a sack and had just two passes defended while not intercepting a pass for the first time in his career.
Woods can play both safety spots and also played as a nickel cornerback as a rookie.
ESPN's Courtney Cronin and Todd Archer contributed to this report.