Dudley took over as CEO of BP on October 1, 2010 amid the biggest oil spill in the US. The company's existence was under threat after 11 people were killed in the Deepwater Horizon catastrophe.
BP, under Dudley, was also working closely with Reliance to develop India's gas resources. Earlier this year, Dudley had said that India will become the world's largest growth market for energy by the mid-2020s and BP was already a large investor in the country.
In June this year, BP and Reliance Industries announced the sanction of the MJ project in the KG D6 block off the east coast of India.
"Bob has dedicated his whole career to the service of this industry. He was appointed chief executive at probably the most challenging time in BP's history," BP Chairman Helge Lund said in a statement.
The Board of BP on Friday said that "Bob Dudley, 64, has decided to step down as group chief executive and from the BP Board following delivery of the company's 2019 full year results on 4 February 2020 and will retire on 31 March 2020".
Dudley will be succeed by Looney, 49, who is currently the chief executive, Upstream. He will join the BP Board on February 5, 2020.
Looney joined BP in 1991 as a drilling engineer and worked in operational roles in the North Sea, Vietnam and the Gulf of Mexico, including as drilling engineer on the discovery of the giant Thunder Horse field, the company said.
After a period in BP Alaska, he became head of the group chief executive's office, working directly for BP chief executives Lord Browne and then Tony Hayward.
( With inputs from IANS )