RedBird Capital Partners completed the deal to purchase a controlling interest in the seven-time European champions for €1.2 billion ($1.2b).
They are the second soccer team the Yankees will partially own (New York City FC in Major League Soccer is the other).
Gerry Cardinale, who founded RedBird in 2014 and is a managing partner, announced a preliminary agreement in June to buy Milan from fellow American firm Elliott Management.
"We have a multi-decade relationship with the New York Yankees and the Steinbrenner family that has resulted in the creation of some of the most successful businesses in sports, entertainment and hospitality," Cardinale said in a statement on Milan's website.
"We are very pleased to continue our partnership with them and will look to explore opportunities together to broaden our fan reach and expand commercial opportunities that are only available to franchises that operate at the highest levels of sports globally."
The closing comes just in time for Cardinale to make his debut as Milan's new president at Saturday's derby against Inter Milan.
"Our vision for Milan is clear: we will support our talented players, coaches and staff to deliver success on the pitch and allow our fans to share in the extraordinary experiences of this historic club," Cardinale said.
"We will look to leverage our global sports and media network, our analytics expertise, our track record in sports stadium developments and hospitality to deliver one goal -- maintaining Milan's place at the summit of European and world football."