General manager Jeff Gorton announced the signing Thursday as prospects skated at the team's Westchester facility.
Halverson appeared in 50 games with Sault Ste. Marie of the Ontario Hockey League (OHL) this past season, posting a 40-5-2 record, along with a 2.63 goals against average, a .913 save percentage and six shutouts.
He is the first Rangers' draft pick in franchise history to earn at least 40 wins in juniors in one season. The 6-foot-4 goaltender posted a 10-4 record in the playoffs.
The Traverse City, Michigan, native represented the United States at the 2015 IIHF World Junior Championship. He was selected by the Rangers in the second round of the 2014 NHL draft.