Rijkman Groenink will step down as chairman of the board once an extraordinary shareholder meeting takes place at a date yet to be set.
ABN Amro is expected to be broken up following the deal.
The 71bn-euro ($98.5bn; £49bn) acquisition marks the largest banking takeover in Europe.
The battle to buy the firm took many months, following a legal row over the future of ABN's US subsidiary.
Initially ABN had backed an offer by Barclays, but it later withdrew its support to leave Barclays and the RBS-led group on an even playing field.
Barclays withdrew its offer last week, leaving the way clear for the RBS group.
