The World Cup-winning striker is the first player to sign for the club, which is jointly owned by Manchester City and the New York Yankees.
Villa, who last month helped Atletico to their first La Liga title, arrives on a three-year deal ahead of the franchise's inaugural MLS season in 2015.
"This is a historic and exciting moment for the City family and the building of New York City Football Club," City CEO Ferran Soriano told the club's official website.
"I know David really well; he is one of the best footballers in the world, a true winner and in an outstanding moment of his career. I'm sure New Yorkers will enjoy watching him play for their city."
Villa, who will wear the No 7 shirt at Yankee Stadium, said: "Throughout my career I've always tried to keep pushing myself to achieve new targets and this represents another important goal for me.
"I want to try and help MLS continue to grow, through playing, working hard, scoring goals and at the same time try to make New York City FC become the best team in the league."
Villa was part of Pep Guardiola's illustrious Barcelona side between 2010 and 2013 and won the World Cup with Spain in 2010.
He could be joined by Frank Lampard, who is out of contract at Chelsea and understood to have held informal talks about a move, as head coach Jason Kreis looks to assemble a stellar first squad ahead of kick-off in March.