Terms of the deal were not disclosed.
The 50-50 partnership was formed in Chicago in 2005 and provides real-time scores, historical information and technology to websites and other customers.
AP and Fox, a unit of Twenty-First Century Fox Inc., will continue to exchange stories, photos and data with Stats.
Ken Dale, AP chief financial officer and senior vice-president, said Stats' revenue has tripled since its founding, but its growth is increasingly in selling technology that is outside AP's core business.
Fox Sports president and chief operating officer Eric Shanks said partnering with AP was a "privilege" while AP president and CEO Gary Pruitt said the venture was "excellent and productive." Both men expressed confidence Stats would continue to grow under Vista.
Dale said AP's revenue and costs won't change significantly after the sale.
The AP will no longer record its share of Stats' profits, which amounted to less than $5 million annually, Dale said.
Proceeds from the sale will be used to cut AP's pension obligations by an amount greater than its typical annual contribution. Dale said the lump sum pension payment will reduce the AP's funding obligation over several years, allowing it to invest more into newsgathering operations.