This includes the internal 'bad bank' with £38 billion of assets like problem loans it wants to run down.
Mr Cullinan, currently chief executive of the bank's Non-Core division, will also be responsible for managing the flotations of Williams & Glyns bank in the UK and Citizens bank in the US and the restructuring of its shipping business. He will report to the group's chief executive Ross McEwan and join its executive committee from 1 January 2014.
Mr McEwan, said: "This new division will help us take the necessary actions on capital and risk to ensure nothing distracts us from making RBS a great customer bank."
Mr Cullinan has led a programme under which RBS has reduced non-core assets by £221bn over the past five years.