The deal is worth $4.5 million, multiple sources confirmed to ESPNNewYork.com, with Hagelin receiving $2.1 million in the first year and $2.4 million in the second.
The agreement with Hagelin is an example of the Rangers' standard "bridge" deal given to players who are coming off an entry-level contract, although they deviated from this salary structure earlier this week when locking up 24-year-old defenseman Ryan McDonagh to a long-term deal.
McDonagh, who has flourished as a leader and top-pair defenseman for the Rangers, signed a six-year contract worth $28.2 million on Monday.
By re-signing Hagelin, whose speed earned him frequent turns with the team's top line this season, the Rangers avoided arbitration with the 24-year-old forward. He had 10 goals and 24 points in 48 games.
The Rangers also reached agreements on a deal Wednesday with newly acquired defenseman Justin Falk.The 24-year-old Falk, acquired by the Rangers from Minnesota on June 30, will earn $975,000 on his one-year contract.
The Rangers have yet to re-sign Derek Stepan, although the center does not have arbitration rights like his fellow restricted free agents do. Forward Mats Zuccarello is arbitration-eligible and expected to file by Wednesday's deadline, a source confirmed.