The Jets announced the signing of the restricted free agent on Sunday. The deal carries an average annual value of $3 million.
Winnipeg acquired Pionk and the 20th overall pick in the 2019 draft for defenceman Jacob Trouba on June 17.
He will be counted on to fill a void for the Jets after trading Trouba and losing defenceman Tyler Myers in free agency.
Pionk, six-foot-190 pounds, went undrafted and was signed as a free agent by the Rangers in May 2017 after two seasons at the University of Minnesota-Duluth.
The 23-year-old from Omaha, Neb., split the 2017-18 season between the Rangers and the American Hockey League before joining New York full time last season.
He produced six goals and 26 points in 73 games in 2018-19.
Winnipeg used the 20th pick from the trade to select Finnish blue-liner Ville Heinola.
The Jets still need to get new contracts done for star wingers Patrik Laine and Kyle Connor.
The Rangers signed Trouba for seven years and $56 million, with an $8 million salary-cap hit for the upcoming season.