The RBS-led group said payment of the offer price of around $50 in cash and 0.296 new RBS share for each ABN Amro share will take place on October 17.
RBS and its partners had effectively won the battle last week when rival bidder Barclays Bank pulled out.
The RBS-led grouping declared its offer as "wholly unconditional" in a statement on Wednesday signifying all its takeover conditions had been met.
The consortium said that shareholders representing around 86 per cent of ABN Amro stock had accepted the bid.
In contrast, Barclays Bank pulled the plug last week on its rival bid worth around $90 bn after securing less than 1.0 per cent of ABN Amro shares.
In recent weeks, analysts had predicted a crushing win for the RBS-led takeover bid because it was higher and mainly in cash, compared with the Barclays offer that was mostly in shares.
The new announcement heralds the break-up of ABN Amro, which dates back to 1824 and once regarded as one of the jewels in the crown of the Dutch economy.
The consortium takeover is also expected to involve the loss of up to 19,000 jobs at ABN Amro.