The linebacker was a free agent after his contract with the Baltimore Ravens came to an end yesterday.
Head coach Rob Chudzinski said in a statement: "We are very excited about the addition of Paul Kruger to our team.
"He is a talented linebacker who is going to make an immediate impact on our defense. When you put on the film, you see physicality, explosive pass rush and a high motor.
"He has been very productive for the Ravens and proved it at the highest level last season in the playoffs."
The 27-year-old's contract is reportedly worth $40m (£26.7m).