RBS said Mr Cullinan will lead its new Capital Resolution Group, the so-called internal “bad bank” that includes £38bn of unwanted assets, which was announced last month.
He had been expected to lead the “bad bank”.
RBS said Mr Cullinan will also have responsibility restructuring the bank’s shipping business and for managing the flotations of Williams & Glyns, a network of 314 branches earmarked for a listing in 2015 or 2016, and Citizens in the United States, which could occur next year.
Earlier this week, RBS cut itself free from an £8bn capital tie to the Government, following recent moves to strengthen its capital base. It was seen as another step along the road to eventual sale.