It marked the second straight day the Rangers came to terms with a young defenseman. On Saturday, New York announced during its 5-1 win over the Buffalo Sabres that the club reached a two-year deal with Dan Girardi worth $3.1 million.
The signing of the 24-year-old Tyutin occurred Sunday just before the Rangers beat the San Jose Sharks 3-1 in another matinee home game. Like Girardi, he would have been eligible for restricted free agency this summer.
Contract terms weren't immediately available.
New York also signed franchise goalie Henrik Lundqvist to a six-year, $41.25 million deal this week.
Tyutin, who has played in all 61 Rangers games this season, has four goals and 14 points. He is in his fourth NHL season after being chosen by New York in the second round of the 2001 draft.