Fridman, Chairman of the TNK-BP Board of Directors, will run the company before the end of the year until a permanent chief executive is selected, the British oil giant said.
Two Russian executives - former Polyus Gold mining group head Pavel Skitovich and Maxim Barsky, managing director of the West Siberia Resources oil company - have been appointed to senior positions in TNK-BP as potential candidates for the post.
The firm's former CEO, Robert Dudley, stepped down in December 2008 after a bitter dispute between the British and Russian shareholders over strategy, management and control of the third-largest oil producer in Russia.
Dudley fled the country in July citing "a campaign of harassment" organized by Russian partners, as the U.S.-backed executive had been barred from working in Russia over labor law violations. The firm was subject to a series of labor checks and tax claims.
Under a deal agreed by the parties on January 9, Dudley was to be replaced by an executive from outside BP with extensive Russian experience.
Fridman is head of the Alfa Group, which is part of the Alfa Access Renova (AAR) consortium of Russian shareholders, holding 50% in the joint venture. BP owns the other half in the oil firm.
