The 36-year-old will earn €113,000-a-week with the newly-formed MLS franchise, where he will join former Barcelona and Atletico Madrid star David Villa on a two-year deal.
"It ticked all the boxes personally for me. It’s a very exciting challenge in life terms," Lampard told reporters at a press conference on Thursday.
"I had a fantastic 13 years at Chelsea but it was a good time for myself and Chelsea that I moved on.
"Having spoken to people at this club and seen the vision - I've seen a real long-term plan and I want to be part of that. I want to keep testing myself."
Goal understands that Lampard agreed terms with New York City FC last month and visited Manchester City's Carrington training base on the same weekend as Villa - with the Premier League champions linked with the MLS club and Melbourne City under the City Football Group umbrella.
New York City FC were also hopeful of landing Barcelona midfielder Xavi although Goal understands the 34-year-old is set to remain at Camp Nou for another season after last-ditch talks with Luis Enrique and president Josep Maria Bartomeu.
Lampard, meanwhile, could follow in Steven Gerrard's footsteps in announcing his retirement from England duty in the coming days.
The midfielder has earned 106 caps for his country but suggested recently that he is considering his international future, with Liverpool skipper Gerrard having announced his decision to end his Three Lions career on Monday.
"In terms of England, my main priority was getting my personal future sorted out" said Lampard. "Now I have to think about England and make a decision. Now I know where I’m playing my football it won’t be long."