Kroenke, who now owns 67% of the club through his company KSE, has put forward a proposal to buy the remainder of the club's shares - 30% of which are owned by Russian billionaire Alisher Usmanov and his company Red and White Securities.
Initially viewed with suspicion by the Arsenal board, the 71-year-old started building his stake in 2007 as he slowly bought out the families who had run the club for generations.
While Kroenke says taking sole ownership will benefit the club, the Arsenal Supporters' Trust (AST) called the news "a terrible day" for the Gunners.
Although a KSE statement explains that taking the club private will help to further Arsenal's "strategy and ambitions", news of the buyout has not been well received by Arsenal Supporters' Trust.
The Arsenal Supporters' Trust said the news marked "a awful day for Arsenal Football Club".
Speculation also emerged in 2017 that Usmanov was looking to buy Kroenke's shares with the minority shareholder reportedly offering £22,000 per share.
The American is the majority shareholder at the Emirates and has this morning launched an "all-cash" offer to acquire 100 per cent control, staging a bid to buy Alisher Usminov's stake in the Premier League club.
The bid will be part funded by a 557 million pound loan from Deutsche Bank.
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"The most awful part of this announcement is the news that Kroenke plans to forcibly purchase the shares held by Arsenal fans".
The American, who owns 67 per cent of the club, has put forward a deal - published via the London Stock Exhange - that will see him buy the remainder of the club's shares.
"KSE is a committed, long-term owner of the club".
"Kroenke's actions will neuter their voice and involvement".
"We appreciate Usmanov's dedication to the Arsenal Football Club and the storied ethos and history the club represents".
Coming at a crucial time for Arsenal as they start life without manager Arsene Wenger for the first time in 22 years, the deal cements the position of the USA sports boss among an elite band of super-rich soccer club owners in England.
"The Arsenal Supporters' Trust is wholly against this takeover", one fans' group said.
Kroenke says he will be raising the capital to take control of the club with £45 million of his own money and borrowing £557 million, which he says will not be secured against Arsenal's commercial operations (unlike the Glazer family's ownership of Manchester United).