Kroenke Sports Enterprises, which has gradually built its stake in the Gunners since first buying 9.9% of shares in 2007, must now bid to buy up the remaining shares after taking their stake to approximately 62.89% after reaching undertakings with major shareholders Danny Fiszman and Lady Nina Bracewell-Smith.
Terms have also been agreed for KSE to buy up the remaining share capital at a cost of ?11,750 a share.
Kroenke said in a statement to the Stock Exchange: "We are excited about the opportunity to increase our involvement with and commitment to Arsenal.
"Arsenal is 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.
"I am delighted that Peter Hill-Wood has agreed to support us by continuing as chairman."
Source: PA