The new team, to be named New York City Football Club (NYCFC), will be the 20th MLS club and is expected to start playing in 2015.
"We proudly welcome two of the most prestigious professional global sports organizations to Major League Soccer<" said MLS Commissioner Don Garber in a statement.
"This is a transformational development that will elevate the league to new heights in this country. The New York area is home to more than 19 million people, and we look forward to an intense cross-town rivalry between New York City Football Club and the New York Red Bulls that will captivate this great city."
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He said: "New York is a legendary sports town, as well as a thriving global city with a rapidly expanding soccer fan-base.
"We are thrilled to contribute to the energy and growth of New York City Soccer. In the Yankees, we have found the absolute best partner for developing a world-class sports organization and a winning team that will carry the New York City Football Club name with pride."
The Premier League club also confirmed that they will be the majority owner of NYCFC, while the Yankees will be an active member of the ownership group.
City are also due to face Chelsea in a friendly match at Yankee Stadium on May 25.
Hal Steinbrenner, managing general partner of the Yankees added: "We are pleased to be associated with this major move by MLS to increase its presence in the New York market and to enhance the opportunity for New York soccer fans to enjoy high-level play in their own city.
"We look forward to the opportunity to work with Manchester City to create something very special for the soccer fans of New York."
New York mayor Michael Bloomberg also added: "Soccer is one of the world’s most exciting and popular sports, and it should be played on the world’s biggest stage - in New York City.
"New Yorkers are the greatest sports fans in the world, and they will welcome a Major League Soccer franchise with the full-throated and loyal support they are famous for.
"Manchester City has a great reputation for both winning teams and serious community investment, and that will help them fit in well with the excellent leadership of New York City’s other professional sports teams.
"Increasingly, sports events and activities - from the NHL playoffs to the MLB All-Star game to the SuperBowl -- are spurring economic growth, as our investments in new arenas and infrastructure are paying off."