Tom Pelissero of NFL Network reports the deal is for one year and $5 million, plus $3 million in incentives.
Wilkerson spent the first seven years of his career with the New York Jets, earning second-team All-Pro honors in 2013 and 2015. The 28-year-old recorded 46 tackles, 3.5 sacks, and an interception in 13 games during the 2017 season.
New York released Wilkerson on February 28.
Wilkerson's final season with the Jets was marred by controversy. He was declared inactive for the team's final game of the season after missing numerous meetings throughout the year.
The veteran defensive lineman will be reunited with Packers defensive coordinator Mike Pettine, who featured in the same role for the Jets from 2009-2012.
Wilkerson can play either defensive tackle or end and his positional versatility is a major asset for the Packers.