"Wei's nomination signalled the central government's recognition of his success in running the group since he became its leader in 1998," the company said in a statement.
Wei was nominated for the position of deputy Party secretary of Hainan by the Communist Party of China and was also chosen as a candidate for the governor of the island province.
Prior to the promotion, the 52-old Fu was vice-president of the company, and also chairman of Hong Kong-listed China Oilfield Services, another subsidiary of CNOOC.