The Jets also acquired forward Patrick Holland in the deal.
The 32-year-old Budaj was 10-8-3 with a 2.51 goals-against average and a .909 save percentage last season in 24 games backing up Carey Price.
The Canadiens' backup goalie is now 25-year-old Dustin Tokarski. He has a 3-3-2 record with a 2.93 goals-against average and a .902 save percentage.
Tangradi played 55 games last season for the Jets, scoring three goals and adding three assists.
- Marc Weinreich