News emerged early on Tuesday that Kroenke had tabled an offer for the club's remaining shares that values the Gunners at £1.8bn after receiving backing from minority owner Alisher Usmanov.
Kroenke already owns 67% of the club through his company KSE, which claims that Usmanov has decided to cash in on his 30% stake.
In line with requirements, the offer was revealed to the London Stock Exchange on Tuesday morning.
A KSE statement read: "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.
The company also added that since "its stewardship since 2011 the club has invested in major transfers, player contracts, analytics, senior non-playing football management employees" and that it "expects the club to build on those investments".
According to 'BBC Sport', Kroenke is financing the offer with £45m of his own money and £557m in loans.
"The offer is not being funded by way of any debt finance (bank loans, payment in kind loans or other debt or quasi debt interest bearing obligations) for which the payment of interest on, repayment of, or security for any liability (contingent or otherwise) will depend on the business of Arsenal," added the statement.