Usmanov bought a 14.58% stake in Arsenal in 2007, eventually increasing that stake to 30% without being granted a place on the board.
The American has reached an agreement with Russian oligarch Alisher Usmanov to take 100% ownership of the Gunners, spending £550 million to take on his boardroom rival's share in the club.
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.
Majority shareholder Kroenke announced on Tuesday morning that he has launched a £600million takeover bid, valuing the club at £1.8billion.
Sky Sports reports that KSE has received an "irrevocable undertaking" from Usmanov's company Red and White Securities "to accept the offer as soon as possible", and by the latest at 3pm today. "KSE is a committed, long-term owner of the club".
Kroenke has been battling Usmanov for control of Arsenal for over a year.
"I think it's very sad that we're in danger of losing any transparency into how our club is run", he told Reuters.More news: Timeline: Tampa mother accused of drowning daughter in Hillsborough River
In a statement, Usmanov said: "I have made a decision to sell my shares in Arsenal Football Club which could be the best football club in the world".
"We appreciate Mr Usmanov's dedication to the Arsenal Football Club and the storied ethos and history the Club represents".
The KSE statement to the London Stock Exchange said taking the club private will help to further Arsenal's "strategy and ambitions".
The news spells an end to a decade-long power struggle in the Arsenal boardroom which culminated in Stan Kroenke's bid to buyout Alisher Usmanov's shares. "Many of these fans are AST members and hold their shares not for value but as custodians who care for the future of the club".
AST added that by becoming the 100% owner, Kroenke would be able to take "detrimental actions" such as paying "management fees and dividends without any check or balance".
It added that it was "in effect legalised theft to remove a brake on how Arsenal is managed".
This is a common thread throughout Kroenke's ownership of sports teams in America too. He owns National Football League team the Los Angeles Rams and NBA team the Denver Nuggets, among others.
Americans have had a mixed fortune as Premier League owners, with the Glazer family rarely popular at Manchester United, even when the club won the league.