"Mr. Considine tendered his resignation in a letter dated August 25th. His resignation will be effective from September 15th," the Russo-British oil venture said in a news release.
The company said Considine was leaving TNK-BP after five years heading TNK-BP's refining, trading and marketing businesses, to pursue other opportunities.
TNK-BP Chief Operating Officer, Tim Summers, said: "We regret we are losing Tony. In his five years of leadership with TNK-BP, he has set an outstanding example of cross cultural performance and success. His team has embodied what TNK-BP was set up to achieve - a unique and powerful blend of Russian and international expertise and talent which leads the industry."
In early August, TNK-BP announced the resignation of TNK-BP Chief Financial Officer James Owen amid an ongoing shareholder dispute.
BP, which holds 50% in TNK-BP, and its Russian billionaire partners have been battling over management and strategy at the joint venture, which is Russia's third largest oil producer and accounts for a quarter of BP's overall output.
CEO Robert Dudley, who has been unable to have his Russian visa renewed, is running TNK-BP from abroad. A Moscow court ruled in mid-August to suspend Dudley from office for two years for violating labor code laws.
The four Russian billionaire shareholders have sought Dudley's dismissal, accusing him of acting only in BP's interests. The British oil major said the Russian investors want to seize control of the company.