The 52-year-old Vigneault is the 35th head coach in the Rangers' 87-year history.
He spent the last seven seasons with the Vancouver Canucks, guiding them to a 313-170-57 record and an appearance in the 2011 Stanley Cup final.
He won the Jack Adams award as NHL coach of the year in 2007.
Vigneault was fired last month after the Canucks were swept in the first round of the playoffs by San Jose.
He replaces John Tortorella, who was fired after the Rangers were ousted by Boston in the second round of the post-season.