McKay, a 34-year BP veteran, will be responsible for strategy and long-term planning, safety and operational risk, technology, and corporate governance.
He will also take on some of chief executive Bob Dudley’s duties.
Currently running BP’s upstream operations, he will be based in London and take up the role after a handover period.
BP chief operating officer for production Bernard Looney will move into McKay’s old job, looking after exploration, development, and oil and gas production.
Katrina Landis, executive vice president of corporate business activities, is also leaving the company.
She will depart on 1 May after 24 years at BP and will not be replaced.
Dudley said the new deputy role would help concentrate BP’s priorities in a tough time for the industry.
BP is the first of the European oil majors to report interim results this week, followed by Royal Dutch Shell and BG Group, with the crude price collapse expected to dent revenues.
BP announced in January it would be forced to cut 4,000 jobs - about five per cent of its global workforce.
“These changes simplify, focus and better align accountabilities within our experienced and versatile senior team,” Dudley said.