Asciano said in July that Brookfield made an indicative offer of A$9.05 per share but on Tuesday said Brookfield upped its offer price to A$9.15 per share, giving it a market capitalization of A$8.9 billion and an enterprise value of A$12 billion.
Further sweetening the offer, Asciano said it will pay a special dividend which effectively values the shares at A$9.54 each, and that it will offer a "mix and match" component so shareholders can choose how much cash or scrip to receive.
"This combination will provide Asciano the scope to leverage our industry leading expertise globally, and the financial capacity to take advantage of the myriad of growth opportunities in our sector," Asciano Chief Executive John Mullen said in a statement.
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Brookfield Infrastructure Chief Executive Sam Pollock said in a statement that "combining Asciano's Australian container terminals with our existing assets in North America and Europe provides the foundation for a global container platform".
Record low interest rates have added to the M&A appeal of the Australian logistics sector which is already struggling with lower valuations because of a downturn in coal exports.
Asciano's former parent company, Toll Holdings, agreed to a A$6.5 billion takeover by Japan Post earlier this year.
Asciano shares have traded at a discount to Brookfield's indicative offer since news broke of the approach as investors questioned whether the company would accept a buyout just as it emerges from a costly restructure aimed at automating its processes and cutting costs amid the coal downturn.
The shares were in a trading halt on Monday after last trading at A$8.11 on Friday, an 11 percent discount to the takeover price. The company said it requested removing its shares from the trading halt on Tuesday.
Brookfield Infrastructure's shares were down 3.5 percent at $40.57 in afternoon trade on the New York Stock Exchange. They fell as much as 7 percent earlier.