The American businessman has also agreed terms for the purchase of the remaining stock which values the club at ?731m.
Kroenke must now bid to buy up the remaining shares after taking their stake to approximately 62.89 per cent after reaching undertakings with major shareholders Danny Fiszman and Lady Nina Bracewell-Smith.
Find out more about the man bringing the American Dream to Arsenal Football Club
Stan's the man: American Kroenke (left0 with chairman Peter Hill-Wood
So, just what changed Peter Hill-Wood's mind.?On Stan Kroenke (2007)'Why don't we want the American at our club? Call me old-fashioned, but we don't need his money and we don't want his sort. Our objective is keep Arsenal English, albeit with a lot of foreign players.
'Americans are buying up chunks of the Premiership football clubs and not because of their love of football but because they see an opportunity to make money.
'They know absolutely sweet FA about our football and we don't want these type of people involved.'
On Kroenke (2011)
'Mr Kroenke has shown himself a man who values and respects history and traditions of this very special club we cherish.'
Terms have also been agreed for KSE to buy up the remaining share capital at a cost of ?11,750 a share.
The move has been sparked by the serious illness of Fiszman, who wants to sell his stake having tied up his affairs in a beneficial trust, knowing his children do not wish to maintain links with the club.
Kroenke Sports Enterprises has gradually built its stake in the Gunners since first buying 9.9 per centof shares in 2007,
Kroenke said in a statement to the Stock Exchange: 'We are excited about the opportunity to increase our involvement with and commitment to Arsenal.
'Arsenal is a fantastic club with a special history and tradition and a wonderful manager in Arsene Wenger.
'We intend to build on this rich heritage and take the club to new success. I am delighted that Peter Hill-Wood has agreed to support us by continuing as chairman.
'We especially wish to acknowledge and thank the board, Danny Fiszman and the Fiszman family as well as Lady Nina Bracewell-Smith and her family for the confidence they have had in me over the past years and in allowing us to move forward in thismore prominent role.'
KSE already own NBA basketball franchise the Denver Nuggets, the Colorado Avalanche NHL ice hockey teamand Major League Soccer side the Colorado Rapids.
KSE have entered into a call and put option agreement with DF Nominees, the company holding Fiszman's stake, to purchase their 16.11 per cent holding and have also received 'irrevocable undertakings' from Lady Bracewell-Smith and other shareholding directorsto sell their shares, totalling 16.79 per cent.
Kroenke's main focus will now be on purchasing the stake of Russian billionaire Alisher Usmanov, who does not have a seat on the board but controls 27 per cent of the club's holding company.
Challenge: Arsenal have gone almost six years without winning a trophy
At this stage it is unclear whether Usmanov would sell. If he retains his stake, he will still wield influence on issues that demand a special resolution.
Gunners boss Wenger welcomed the newsof Kroenke's deal and said: 'I have worked with Stan Kroenke at board meetings over the past couple of years and I believe he has the best interests of Arsenal at heart.
'He understands the club's heritage and traditions and our ambition to run the club in a way which protects our long-term future.'
Speculationis rife that Kroenke's move could lead to the return of former vice-chairman David Dein.
Wenger has missed Dein's counsel since he was forced off the board for introducing Kroenke to the club, having brokered the deal for the American to buy the 9.9 per cent stake that was owned by ITV. Yet Dein then sold his stake to Usmanov.
Long-term view: The Emirates Stadium has provided huge revenue for Arsenal
Who is Stan Kroenke?Age: 63
Lives: Columbia, Missouri.
Wife: Anne Walton Kroenke, is daughter of the Wal-Mart founder Bud Walton.
Education: Masters degree in Business Administration, BA and a BSc from University of Missouri.
Estimated value: $3bn (?1.8bn). Bought into Arsenal in April 2007 and joined the board of directors in September 2008. Has been steadily increasing his stake since.
What he owns.
Sports teams: Denver Nuggets (basketball), Colorado Rapids (soccer), Colorado Avalanche (ice hockey), St Louis Rams (American football) and Colorado Mammoth (lacrosse).
Sport and entertainment: PepsiCenter, Denver Dick's Sporting Goods Park, the Paramount Theatre, OdeumColorado concert hall.
Others: A television company, ArsenalBroadband Ltd (50 per cent), a ticket company, hotels, ranches, wineries, real estate and houses across North America.
The move could force Wenger to cave in to demands for pre-season tours in the US, but there is hope Kroenke would inject cash into the transfer kitty.
Arsenal chairman Hill-Wood, who initially said the Gunners did not want Kroenke's 'sort' involved at theclub when KSE bought their initial stake four years ago, added: 'The board of directors and I consider it a key responsibility to protect theethos and spirit of the club.
'Mr Kroenke, although relatively new to Arsenal, has shown himself to be a man who values and respects the history and traditions of this very special club that we cherish. We areconfident that he will be a safe custodian of its future.
'At this time of transition I would like to pay particular tribute to Danny Fiszman for his immense contribution. Danny's vision and drive led the relocation to our new stadium, an historic move which will benefit the club and its many passionate fans long into the future.
'I would like to pay tribute to the important and long-standing role that the Bracewell-Smith family have played in Arsenal's history.
'The family have been staunch supporters of the club for over 70 years and the club is significantly indebted to them for the role that they have played in its development and success. We will be considering appropriate ways to mark this long and valued contribution.'
There is concern from Arsenal Supporters' Trust over the club being taken into private ownership, which would essentially be the case if Kroenke ends up with more than 75 per cent. Small shareholders currently retain around 12 per cent.
The AST's Tim Payton said: 'Arsenal is a stronger institution when supporters are directly involved in its ownership structure. Stan Kroenke has always been a supporter of the AST and supporter shareholders. We expect him to involve us in talks about any plans he has.'
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Explore more:People: Danny Fiszman, Peter Hill-Wood, Nina Bracewell-Smith, David Dein Places: Denver Organisations: National Basketball Association, Arsenal Football Club