Stafford was let go by the Wild on Friday having failed to turn his PTO into a permanent contract.
Stafford agreed to terms on a professional tryout agreement with Minnesota on Wednesday.
Stafford was held scoreless in Saturday's 4-3 overtime win over Florida, finishing the season with five goals and 13 points in 57 appearances.
Stafford failed to mark the scoresheet during Friday's 5-4 win in Minnesota, pushing his point drought to five games.
Stafford recorded two shots and a minus-1 rating over 10:49 of ice time in Tuesday's 5-1 loss to Buffalo.
The Devils activated Stafford off injured reserve Saturday.
Stafford (upper body) isn't in the projected lineup for Thursday's game against Detroit.
Stafford (upper body) will not accompany the team on its upcoming seven-game road trip, Amanda Stein of the Devils' official site reports.
Stafford didn't make the Devils' 23-man roster and will become a free agent, Mike Morreale of NHL.com reports.
Stafford will join New Jersey at training camp on a professional tryout.