Lamaprd has penned a two-year-deal with the franchise, who are owned by Premier League champions Manchester City.
The England international heads to the United States ahead of their first season in the competition in 2015.
Lampard, 36, joins David Villa, Spain's record goalscorer, at the City Football Group-owned side.
He had been without a club since he left Chelsea in June after a successful 13-season stay with the Premier League giants.
Chelsea's all-time leading goalscorer represented England during their disappointing World Cup campaign in Brazil, making one appearance in the 0-0 draw with Costa Rica in their final group fixture.
Lampard said: "Having spoken to the people from the club here and seeing the vision, I'm not talking about a franchise hoping things come off, I've seen a real long term plan and I want to be a part of that.
"I want to be that leader - I want to be that person - not just on the pitch but off the pitch too."
"I had a bit of time after the World Cup which was a huge disappointment," the veteran midfielder added.
"I know I need to think about England, I know need to think about that but it won’t be long now I know where I’m playing my football I can make that decision."
"I'm going to keep fit," he explained. "How I'll do that is not clear yet I’m going to sit with [director of football operations] Claudio [Reyna] and [head coach] Jason [Kreiss] and find the best way forward."
