ADM said on Monday that it acquired an additional 5 percent of GrainCorp for the new offer price, raising its stake in the Australian grains handler to 19.9 percent.
It said it was ready to begin due diligence on a takeover immediately.
GrainCorp knocked back ADM's earlier bid, which valued the company at $2.8 billion, saying it undervalued GrainCorp after a bumper harvest delivered a record annual net profit. At the time, analysts and shareholders had said they expected a higher offer.
Reporting by Martinne Geller in New York; Editing by Lisa Von Ahn and Gerald E. McCormick