The New York Rangers were able to renew one of their players to a new deal and held on to a defenseman they picked up in late June.
Hagelin agreed to a two-year, $4.5 contract. He will earn $2.1 million next season and $2.4 million in 2014-15. He carries a salary-cap hit of $2.25 million.
The 24-year-old Falk, acquired by the Rangers from Minnesota on June 30, will earn $975,000 on his one-year contract.
These new deals come a couple days after picking up their more talented defenseman, Ryan McDonough, for a six-year, $28.2 million extension.
Hagelin has played with the Rangers for a total of two seasons, including all the games last season. He finished the season with 10 goals and 14 assists for 28 points on the year. The forward is one of the better players when it comes to shots on goals, ranking 37th nationally with 132 in the regular season.
Falk has spent the last four years with the Wild. He had 40 penalty minutes and three assists with zero goals last season.