Under the recommendation of the company's board of management, she would also become a managing director of the Shell Petroleum Co. Ltd. and a group managing director of the Royal Dutch/Shell Group of Cos.
Her appointment is expected at the shareholders' meeting June 28.
Cook, an American, joined Shell Oil Co. in Houston in 1980.
She worked for the company here and California in a variety of technical and managerial positions until 1998, when she moved to The Hague to become director of strategy and business development on the Shell Exploration and Production Global Executive Committee.
In 2000, Cook was appointed CEO for Shell Gas & Power in London.