The approval for the deal comes at a time when banks are experiencing steep falls in the price of shares amid escalating worries about exposure to the sub-prime mortgage market.
This development had led some analysts to propose that market turbulence might stymie the takeover.
However, a spokesman for RBS denied that ABN Amro had any significant exposure to the troubled US mortgage sector and remained viable.
RBS chairman Tom McKillop said: "We believe ABN is a very responsibly run bank and we have no reason to believe they have any undue exposure."
Meanwhile, Barclays Bank - which is vying with a consortium led by RBS for the takeover of the Dutch bank - is expected to receive approval from the Dutch Financial Ministry today.
The British bank's bid will be given a "declaration of no-objection" to approve the takeover, according to a report from the Reuters news agency.