KSE said the holders of the remaining 3 percent of Arsenal will be entitled to receive 29,419.64 pounds for each share.
Most of that is held by Russian businessman Alisher Usmanov, through Red and White Holdings, which KSE said had given an "irrevocable undertaking.to accept the offer".
The main Arsenal fan group said Kroenke mounting full control "marks a terrible day" for the club, which is preparing for its first season with Unai Emery as coach after Arsene Wenger's 22-year reign ended.
"We at KSE are moving forward with this offer leading to 100 percent ownership of the club", Kroenke said in the LSE statement.
"KSE is a committed, long-term owner of the club".
Aside from its stake in Arsenal, KSE also owns a number of U.S. sports clubs across a number of codes including; the Los Angeles Rams in American Football, the Colorado Avalanche in ice hockey and the Denver Nuggets in basketball.
But the Arsenal Supporters' Trust set out its opposition to the proposed move.
And the Arsenal Supporters' Trust has voiced several concerns over the potential takeover in a strongly-worded statement of their own.
Prepare for $90 oil after sanctions against Iran take effect
China, Russia and Turkey have already indicated that they would not comply with the unilateral United States sanctions. He also praised the "most biting sanctions ever imposed" and said they would "ratchet up to another level" in November.
Mr Usmanov has been critical of Mr Kroenke's running of the club on and off the field.
Initially viewed with suspicion by the board, Kroenke started building up his position from 2007 as he slowly bought out the families who had run the 132-year-old club for generations.
Kroenke will be raising the capital to take control of the club with £45m of his own money and borrowing £557m, which he says will not be against the club.
'It is in effect legalised theft to remove shareholder scrutiny on how Arsenal is managed.
Arsenal have endured a hard period on the pitch in recent seasons, last winning the league in 2004 and failing to qualify for the lucrative Champions League for the past two seasons.
Kroenke now holds 41,743 Arsenal shares, approximately 67.09 per cent of the club.
The statement added: "KSE's ambitions for the club are to see it competing consistently to win the Premier League and the Champions League, as well as the major trophies in the women's senior game and at youth level".
New manager Unai Emery, who joined from Paris St Germain, will be given a baptism of fire this weekend when Arsenal kick off their new season against Manchester City.