Wilkerson, 28, is a seven-year veteran with the New York Jets. He started 101 of his team's 112 games and has 44.5 sacks on his career.
His best years were in 2013 and 2015, with 10.5 and 12 sacks respectively, but has only eight sacks the past two seasons.
Defensive coordinator Mike Pettine helped mentor Wilkerson during his first two years in the NFL, part of Pettine's four-year tenure before moving on to Buffalo in 2013.
Reports say that he has had a tendency to "take plays off," arrive late at meetings and underachieve in the past. The Jets released him after his last two seasons.
The Packers had the second-worst opposition passer rating in the NFL in 2017, in a league where the ability to throw the football often dominates whether you win or lose. If Wilkerson plays motivated every play, he could be a force.