The deal is worth a shade over $4.4 million per season, according to Sportsnet's Elliotte Friedman.
Chytil is in the midst of a breakout campaign, recording a career-high in goals (22), assists (20) and points (42) this season while appearing in 66 games. The 23-year-old is the seventh Rangers player in the past 20 years to record a 20-goal season at age 23 or younger, per the team.
The Czechia native was drafted by the Rangers 21st overall in 2017.
New York is firmly locked into a playoff position in the Eastern Conference and is still in the mix to win the competitive Metropolitan Division. The Rangers currently have 98 points, narrowly trailing the Carolina Hurricanes (103 points) and New Jersey Devils (100 points) with eight games to play.