Financial terms were not disclosed. Skjei, who was a restricted free agent, had been scheduled for an arbitration hearing Tuesday.
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The 24-year-old defenseman had 25 points (four goals, 21 assists) in 82 games with the Rangers last season.
"I think I'll play a few more minutes this year," Skjei said this month before agreeing on his contract. "I'll try to bring the best I can bring to the table. ... All the younger guys have a chance to step up. We have a lot of guys that can really prove themselves this year, and I'm excited for that."
The Rangers selected Skjei in the first round (No. 28) of the 2012 NHL Draft. He has 64 points (nine goals, 55 assists) in 169 NHL games and seven points (four goals, three assists) in 17 Stanley Cup Playoff games.
New York has an arbitration hearing scheduled with center Kevin Hayes on Aug. 2, and with center Ryan Spooner on Aug. 4. Forward Jimmy Vesey avoided arbitration when he agreed to terms on a two-year contract with the Rangers on July 17.