Kroenke has been the majority shareholder at the North London outfit in 2011, and an offer to purchase the shares of Alisher Usmanov - who held the next highest stake - was made earlier this year.
That bid was accepted, and that has led to Kroenke acquiring the remaining 2.86% which was held by a number of minority shareholders.
A statement from NEX - where Arsenal's shares are traded - read: "Further to the announcement made by KSE, UK, Inc. on 28 August 2018 confirming the closing of its offer for Arsenal Holdings PLC, the compulsory acquisition by KSE of all of the Arsenal shares not assented to the offer completed on 25 September 2018.
"As stated in KSE's announcement on 28 August, the trading in Arsenal shares on the NEX Exchange Growth Market will be withdrawn with effect from close of business today."
Kroenke also has involvement in a number of American sports teams, including MLS side Colorado Rapids.