The deal values the smaller firm at just under $1.7 billion, 29 per cent above Benfield's closing price yesterday.
Shares in the UK-listed broker also improved a further 30 per cent this morning as the markets reacted to the news, Reuters reports.
The bid - which would see Benfield incorporated into Aon's reinsurance business, Aon Re Global - has already been agreed unanimously by both boards.
Reductions in administrative costs are thought to be a major factor behind Benfield accepting the offer, with around $130 million a year in savings anticipated by both firms by 2011.
Benfield chief executive Grahame Chilton said: "This is fair value for both parties...[it] will be recognised as good value to [our] shareholders."
Greg Case, president and chief executive of Aon, commented: "This agreement reflects our ongoing efforts to ensure that Aon's colleagues, capabilities and technology remain at the forefront of our industry and that we provide the best value for our clients."
Aon is the world's largest insurance broker.