The 21-year-old forward, who was a restricted free agent, scored 22 points (eight goals, 14 assists) in 42 games last season.
Selected by New York in the first round (No. 21) of the 2017 NHL Draft, Chytil has scored 71 points (34 goals, 37 assists) in 186 regular-season games, and has not scored a point in three Stanley Cup Playoff games.
The Rangers signed defensemen Patrik Nemeth (three years) and Jarred Tinordi (two years), and forward Greg McKegg (one year) on Wednesday. Financial terms were not disclosed.
Nemeth scored 10 points (three goals, seven assists) in 52 regular-season games for the Detroit Red Wings and Colorado Avalanche last season. The 29-year-old has scored 58 points (eight goals, 50 assists) in 366 NHL games.
Tinordi had one assist in 21 games with the Nashville Predators and Boston Bruins last season. The 29-year-old has scored 12 points (one goal, 11 assists) in 102 NHL games.
McKegg scored one goal in five games with the Bruins last season. The 29-year-old has scored 34 points (19 goals, 15 assists) in 190 NHL games.
