Katie Strang of ESPN.com reports Hagelin's deal is for two years and $4.5 million; he will receive $2.1 million for 2013-14 and $2.4 million in 2014-15.
"I am honored to be a part of the Rangers organization," Hagelin told Blueshirts United from his home in Sweden on Wednesday. "I love the guys on the team, they truly are all my friends, and I am pumped to get going next year with them."
Hagelin, 24, recently completed his second NHL season recording 10 goals and 24 points, playing in all 48 regular-season games for the Rangers. He added three goals and six points in 12 Stanley Cup Playoff games. He had surgery to repair a torn labrum in his left shoulder on May 31.
"I have been doing a lot of biking, and usually I like to run throughout the summer, so that's been one difference, but everything is going the right way in regards to the shoulder," Hagelin said. "It's been six weeks since the surgery so I can't wait to get that sling off here in the next few days, and then work on getting my range of motion back and take it from there. I am confident my shoulder will be better and stronger next season."
Hagelin has career totals of 24 goals and 62 points in 112 regular-season games, and three goals and nine points in 29 postseason games.
During the Stanley Cup Playoffs, coach John Tortorella said Hagelin "stinks" on the power play. Tortorella was fired after the season and replaced by Alain Vigneault.
"I'm just going to go in and do my job and he'll do his job," Hagelin said of his new coach. "He's a great coach who obviously has that winning mentality. That's always great to play for a coach like that. He's pretty offensive minded, too, so I am really excited to get a good start to the season and show him what I can do."
Strang reports Falk's contract is for one year at $975,000. The 24-year-old was acquired from the Minnesota Wild on June 30 in exchange for forward Benn Ferriero and a sixth-round pick in that day's NHL Draft.
Falk had three assists in 36 regular-season games for the Wild last season and was scoreless in four playoff games. He has one goal and 15 points in 108 career regular-season games.