The Wild announced the deal Sunday with the restricted free agent.
Haula had seven goals and seven assists in 72 games last season while playing mostly on the fourth line. He added one goal while appearing in two playoff games.
The 24-year-old Finn was a seventh-round draft pick in 2009 out of the University of Minnesota. He was more productive in his rookie season with six goals and nine assists in 46 games. The speedy center had a breakout performance in the 2014 playoffs with four goals and three assists in 13 games.