News broke Friday evening, via TSN's Aaron Ward, that Vigneault had notified the Dallas Stars that he is no longer available for their coaching vacancy.
The Stars had made Vigneault a significant offer to become their next coach, but he rejected the deal to accept the post in New York.
It's unclear when the Rangers will make an official announcement.
Vigneault, 52, met with Rangers GM Glen Sather and his staff at the club's organizational meetings in La Quinta, California, on Tuesday.
The Rangers also met with former captain Mark Messier, who could join Vigneault's staff as an assistant, TFP has learned. Such a move, though, is not set in stone, as Vigneault will be responsible for hiring his own coaching staff.
Vigneault became the 16th Head Coach in Canucks history on June 20, 2006. During his tenure, he led the Canucks to two Presidents Trophies, a Stanley Cup Final appearance, and six Northwest Division titles and post-season berths in all seven seasons with the club.
Vigneault, the Canucks' franchise leader in regular-season wins as a head coach, was presented with the Jack Adams Award as NHL Coach of the Year at the 2007 NHL Awards in Toronto.
He was the coach of the Canucks' AHL affiliate, the Manitoba Moose, before jumping on with the Canucks.
Prior to joining the Canucks' organization, he served as head coach of the Montreal Canadiens from 1997-2001, becoming the organization's second youngest coach in club history at the age of 36.