The Vikings on Monday announced the deals, which were pending completion of a physical exam. Alexander made a quick return to Minnesota, which drafted him in the second round in 2016 out of Clemson. He left as a free agent last year for Cincinnati, where he started 10 games in the nickel role.

The Vikings mostly used Jeff Gladney, one of their 2020 first-round draft picks, in the slot when they had five defensive backs on the field last season. By bringing in Alexander and eight-time Pro Bowl pick Patrick Peterson, the Vikings have lessened the pressure on Gladney and Cameron Dantzler, who showed signs of promise in their first year but were often overwhelmed as rookies.

Woods played his first four seasons for Dallas after being drafted in the sixth round in 2017 out of Louisiana Tech. In 2015, his college position coach was Karl Scott, who was hired by the Vikings this winter as their defensive backs coach. Woods became a full-time starter in his second year and has 18 passes defensed, five interceptions and three forced fumbles in his career.

He’ll fill the spot vacated by Anthony Harris, who signed with Philadelphia. Five-time Pro Bowler Harrison Smith has manned the other safety spot for nine seasons.

While the lack of a pass rush was a glaring problem, the secondary was more vulnerable last year than ever since Mike Zimmer was hired as head coach in 2014. The Vikings finished 2020 without a single cornerback who had played in more than 28 career games. The additions of Peterson and Alexander will make it tougher for Mike Hughes to stay on the team. Their 2018 first-round draft pick has been limited by injuries his entire time in the NFL, with neck trouble setting him back in each of the last two seasons.