Under the terms of the deal Barclays has offered $49.25 per share, equating to a market capitalization of $95 million for ABN Amro.
Meanwhile, the two banks have also agreed that ABN Amro will sell off LaSalle Bank to Bank of America in a cash deal worth $21 billion.
A statement from the banks said: "The proposed merger of ABN Amro and Barclays will create a strong and competitive combination for its clients with superior products and extensive distribution. The merged group is expected to generate significant and sustained future incremental earnings growth for shareholders."
The two banks also confirmed earlier reports that the new venture will be headquartered in Amsterdam, with Barclays' John Varley installed as chief executive officer while Bob Diamond taking up the position of president.
However, despite news that Barclays' offer has been accepted, ABN Amro is still set to press ahead with talks with Royal Bank of Scotland, Banco Santander Central Hispano and Fortis, to which it had agreed just over a week ago.