He pointed out that until a shareholder vote takes place, another bidder can technically still come forward.
He said: "We will now move forward with Silver Lake and ValueAct Capital unless a proposal is received that is superior to the present offer."
The company is now planning a shareholder meeting to vote on the offer, which is set at $27.10 per share. It is awaiting clearance on minor matters from the US Securities and Exchange Commission before it can set the date.
The approval of a two-thirds majority of shareholders will be needed for the acquisition to go through.
The company's second largest shareholder, MMI Investments, has said it will vote against the offer, claiming it undervalues the company. It criticised the board for not doing enough to attract an improved offer. It owns less than 12.9% of Acxiom shares.
In addition, another shareholder, Levy Investments, has filed a lawsuit seeking to block the sale.
The offer has prompted speculation about the future of Acxiom's European business and whether the likely new owners would retain it or sell it off.