Mr Usmanov has been critical of Mr Kroenke's running of the club on and off the field.
"18,695 Arsenal shares (representing approximately 30.05 per cent) for an agreed price of £29,419.64 per share in cash valuing Red and White Securities' stake at just over £550m".
"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", Kroenke's company said.
Usmanov has also released a statement and said: "I have chose to sell my shares in Arsenal Football Club which could be the best football club in the world".
In a world where clubs are owned by billionaires who do not always turn up to watch them play, the independent shareholders formed a rare bridge between the club's board and its fans.
In October a year ago KSE offered around £525million to buy the 18,695 shares held by Usmanov.
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He spent a few hours in a local jail cell until he sobered up, but was not formally charged. After pleading no contest, he was sentenced to 150 days in the Los Angeles County Jail.
While Kroenke says taking sole ownership will benefit the club, the Arsenal Supporters' Trust (AST) called the news "a terrible day" for the Gunners.
The club last won the Premier League in 2004.
Apart from Arsenal, Kroenke's "family portfolio" of assets also include NFL side Los Angeles Rams, the NBA's Denver Nuggets, the NHL outfit Colorado Avalanche, MLS side Colorado Rapids and Colorado Mammoth of the National Lacrosse League. However, the prospect of the North London club being owned by one man, particularly when that one man is Kroenke, is worrying for all associated with the Gunners.
But the Arsenal Supporters' Trust (AST) said it was a "dreadful" day for the club, adding it was too important to be owned by one person.
"We appreciate Mr Usmanov's dedication to the Arsenal Football Club and the storied ethos and history the club represents", he said.
Kroenke said in a statement: "We at KSE are moving forward with this offer leading to 100% ownership of the club".
"The AST is also extremely concerned to note that this purchase is being funded by a loan", it added.
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 which marks a very sad day for Arsenal Football Club".