The 36-year-old Lampard left Chelsea in June after 13 years with the London club where he won three Premier League titles, four FA Cups, two League Cups, the Europa League and the Champions League.
"It is a very exciting challenge for me in life terms. I had a fantastic 13 years with Chelsea that I can look back with pride upon. Having seen the vision here, seeing a real long-term plan, I wanted to be part of that. I want to carry on challenging myself and be a leader not only on the pitch," Lampard told a news conference.
"He is a professional, a leader and he ticked all the boxes in terms of the qualities to help grow our team," said New York sporting director Claudio Reyna.
The midfielder said he had yet to make a decision on his England future having focused on resolving his club situation first.
New York City are owned by England's Manchester City and Major League Baseball's New York Yankees and will play at Yankee Stadium when the 2015 MLS season gets under way in February.
Lampard said no decision had yet been made on what he would do between now and the start of the 2015 season.
Villa will play for another City-owned club, Australia's Melbourne City FC, before teaming up with New York but Reyna said there were a "number of options".
"This is a very exciting challenge for me," said Lampard.
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