According to Larry Brooks of the New York Post, the deal is worth $5.25 million per season for a total of $31.5 million.
After three successful seasons at the University of Minnesota, Skjei got his first taste of NHL action with the Blueshirts during the 2015-16 season.
His first full NHL campaign came in 2016-17, and he acquitted himself well, finishing 10th in the voting for the Calder Memorial Trophy, which is given to the league's top rookie.
In 80 games, Skjei racked up five goals and 34 assists to go with a plus-11 rating. He also added five points in 12 playoff contests.
The drop-off was steep for Skjei and the Rangers as a whole last season, however. In 82 games, he finished with four goals and 21 assists, as well as a minus-27 rating.
With just 77 points, the Rangers finished last in the Eastern Conference's Metropolitan Division.
New York dealt franchise defenseman Ryan McDonagh to the Tampa Bay Lightning amid their struggles, which made Skjei the de facto No. 1 guy on the blue line.
While New York has established veterans on defense in Kevin Shattenkirk and Marc Staal, Skjei's combination of youth and two-way ability suggests he will be the Rangers' top defenseman for the foreseeable future.