Kroenke currently owns 67% of the Gunners through his company Kroenke Sports & Entertainment.
However, the American billionaire has offered to purchase the remaining 30% owned by Alisher Usmanov, with the buy-out announcement made to the London Stock exchange on Tuesday.
"We at KSE are moving forward with this offer leading to 100% ownership of the club. We appreciate Mr Usmanov's dedication to the Arsenal Football Club and the storied ethos and history the club represents," read the statement.
"The successful implementation of the offer will result in the opening of a new chapter in the history of the club in bringing 100% private ownership by KSE.
"KSE believes moving to private ownership will bring the benefits of a single owner better able to move quickly in furtherance of the club's strategy and ambitions. KSE is a committed, long-term owner of the club."
The Gunners will open their 2018-19 Premier League campaign at home to the champions Manchester City on Sunday afternoon.