The American sports mogul, who already owns 67 per cent of Arsenal through his company KSE, has reached a deal with Russian billionaire Alisher Usmanov for the sale of his 30 per cent stake, according to a statement to the London Stock Exchange.
"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," it said in the statement.
"KSE is a committed, long-term owner of the club".
Kroenke, owner of the Los Angeles Rams American football team, has been a part-owner of Arsenal since 2007, gradually increasing his stake in the club since.
Uzbekistan-born Usmanov, who made his fortune in the steel industry, had reportedly made previous bids to take control of the club but was repeatedly rebuffed.
He was critical of Kroenke's passive ownership style, which has been increasingly echoed by Arsenal fans unhappy with what they see as the board's willingness to settle for on-field mediocrity so long as commercial stability was maintained.
Under takeover rules, if Usmanov accepts the offer it would trigger the sale of the remaining minority shareholders' shares, many of whom have preserved a small holding for decades, and place the club under the private control of Kroenke.
"We at KSE are moving forward with this offer leading to 100 per cent ownership of the club," Kroenke said in the LSE statement.
"We appreciate Mr Usmanov's dedication to the Arsenal Football Club and the storied ethos and history the club represents."
Further detail of the all-cash offer will be published by KSE later on Tuesday, it said.