Kroenke, who currently owns a 29.98% stake in Arsenal, has agreed to acquire shares from Danny Fiszman and Lady Nina-Bracewell-Smith who each own 16% to bring his total holding to 62.89%.
The move will value Arsenal at about £731m and make it the tenth Premier League club under foreign ownership.
Kronke first became an Arsenal shareholder in 2007 and increased his 9.9% stake to 29.9% in 2009 – just short of the amount required for a formal takeover offer.
The majority of the remaining shares left for Kroenke to purchase are held by Russian billionaire Alisher Usmanov whose Red and White Holdings has a 27% stake in Arsenal’s holding company. If Usmanov opted to relinquish these shares, Kroenke would hold 89% of the club.
Kroenke also owns US sport franchises including the Denver Nuggets basketball team, the Colorado Rapids football team, the NHL’s Colorado Avalanche and the St Louis Rams American football team.
In a statement issued to the London Stock Exchange today, Kroenke says: “Arsenal are a fantastic club with a special history and tradition and a wonderful manager in Arsene Wenger. We intend to build on this rich heritage and take the club to new success.”
Arsenal are currently second in the Premier League and are seeking to end a six-year trophy drought.
Other Premier League teams have also attracted interest from the US. American basketball star LeBron Kames acquired a minority stake in Liverpool Football club, last week. Manchester United and Aston Villa are also both under American ownership.