The consortium, which also includes Fortis and Santander, is due to reveal details of its purchase of 40.76 million shares to shareholders today.
The buying spree began last Friday and was finished yesterday morning to take advantage of a temporary slide in ABN Amro's share price.
RBS is believed to have spent $1.35 billion on the deal.
A statement from the bank said that the transaction is intended to "send a clear message to the market of our intention to buy ABN".
News of the developments comes as Barclays this week announced that it had received approval from the Dutch Financial Ministry for its bid for ABN Amro.
Should either bid be accepted it would represent the largest cross-continental banking transaction ever enacted, with the consortium's offer standing at $97 billion - compared with Barclays bid of $87 billion.