Andy Inglis, the head of the company's upstream business, will leave the company at the end of the year, BP said in a statement.
"These are the first and most urgent steps in a programme I am putting in place to rebuild trust in BP – the trust of our customers, of governments, of our employees and of the world at large,"
Dudley, 55, takes over as CEO later this week. He is charged with rebuilding the company's sullied image following the Gulf oil disaster, which saw BP accused of cutting corners on safety.
BP's investigation into the Gulf oil disaster said BP shared blame for the accident with other companies including Halliburton Co. (HAL), which cemented the well, and Transocean Ltd. (RIG), which operated the oilrig.