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.
Kroenke first bought up a 10-percent stake in 2007, which gradually increased to close to 30 percent by 2009.
He said on Tuesday he had now received an acceptance from Usmanov to buy his 30 percent stake, adding to the 67 percent he already owns.
The American billionaire's decision to make his latest offer comes from his belief that taking the club private with a single, long-term owner will benefit them with respect to moving quicker in accordance to their strategy and ambitions.
Mr Usmanov will receive £550m for his holding, based on the share price of £29,419.64.
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Arsenal finished the 2017/18 season in sixth place behind the two Manchester clubs, fierce local rivals Tottenham Hostpur, Liverpool and Chelsea.
"Many of these fans are AST members and hold their share not for value but as custodians who care about the future of the club".
Mr Kroenke, through his wholly-owned Kroenke Sports & Entertainment, now holds a 67% stake in the London club.
Mr Kroenke, who owns the Los Angeles Rams American Football team and Denver Nuggets basketball teams, said: "We at KSE are moving forward with this offer leading to 100% ownership of the Club".
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"Kroenke's actions will neuter their voice and involvement".
"Unfortunately, I have no control in this club", Usmanov told CNN in 2015.
Wright wrote: "Incredibly sad day for so many of our fan shareholders that that no longer own a part of this club Imagine if this wasn't only about but about the club, the community & the fans - all this new enthusiasm we are witnessing with Unai wouldn't feel like such a waste".
Stan Kroenke's takeover of Arsenal could put his personal fortune at risk if he fails to keep up repayments.
"The AST is wholly against this takeover".
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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). "Arsenal remains too important to be owned by any one person".