The row has focused attention on the rights of foreign investors in Russia.
BP has signed an agreement aimed at solving a festering dispute over control of its Russian venture TNK-BP.
The boss of TNK-BP, Robert Dudley, will step down as part of the deal with the Russian billionaires that control half of the business.
Three independent directors will also be appointed to TNK-BP's board.
Mr Dudley's departure had been central to the power struggle between BP and the Russian investors in the venture, which accounts for 25% of BP's profits.
The memorandum of understanding, signed on Thursday, also includes the option to list up to 20% of the venture on international markets.
TNK-BP's Russian partners had long called for Mr Dudley's departure and Mr Dudley left Russia in July in the face of what he said was "sustained harassment".
BP said it had agreed to offer a Russian-speaking candidate for the post, with extensive Russian business experience.
The Russian shareholders had accused BP of running TNK-BP like a subsidiary and Mr Dudley of favouring the British shareholder.
BP chairman Peter Sutherland said that the agreement, to be finalised over coming months, would relieve recent tensions between the two sides.
"It will create a stable base from which to grow the joint venture to the benefit of everyone involved, including the Russian state," Mr Sutherland said
He said that Mr Dudley had been an outstanding chief executive and would be hard to replace.
BP owns 50% of the venture while the Russian shareholding is made up of a number of Russian billionaires who control a consortium known as Alfa Access Renova (AAR).
Russia welcomed the compromise between AAR and BP.
"We are pleased that this situation has been resolved and the shareholders have come to an agreement without the involvement of third parties, including the state," said Igor Sechin, Deputy Prime Minister of the Russian Federation.
"This is a positive signal for the Russian market. We support the development of TNK-BP and believe that this company has excellent long-term prospects."
Viktor Vekselberg, chairman of Renova, said the agreement was the result of difficult negotiations.
"Most importantly, emotions were not allowed to prevail over common sense and both sides found the solution that best meets the interests of TNK-BP," he said.