Considine's resignation follows a decision earlier this month by the company's chief financial officer, James Owen, to leave amid a months-long dispute between the company's owners.
Considine, who headed TNK-BP's refining, trading and marketing businesses, will leave the company on Sept. 15, TNK-BP said in a statement.
"Tony's family moved back home to Australia at the end of last year, as his children had to get their education there, and Tony wants to follow them," TNK-BP spokesman Peter Henshaw said by telephone Monday.
"Tony also felt he could no longer contribute to the work of the company," Henshaw said.
The candidate to replace Considine has to be formally picked by the chief executive and then approved by the board, which might prove problematic because the British and Russian owners are expected to lobby for their own candidates to fill the job.
TNK-BP is 50 percent owned by British oil giant BP and a group of Russian billionaires, represented by a company called AAR. The two sides are embroiled in a control dispute, with the Russians complaining that too many foreigners hold senior positions in the company, among other things.
AAR chief executive Stan Polovets said the appointment of Considine's successor should be the prerogative of a new independent CEO empowered to assemble his own management team without obligation to hire from either group of shareholders.
Current CEO Robert Dudley is living outside Russia after a Russian court earlier this month barred him from holding the position for two years over alleged labor violations. BP has said Dudley would continue to run the company from abroad.
No candidates to replace Considine have been considered, Henshaw said.
A source close to TNK-BP suggested that one of the reasons for Considine's resignation was negative implications from the shareholders dispute.
BP spokesman Vladimir Buyanov declined comment on Considine's departure, saying only, "Tony contributed a lot to the company, and we wish him success in future."
Polovets expressed regret on behalf of AAR. "Tony has made an outstanding contribution to the company, and we wish him success in his future endeavors," he said, adding, "We have been aware for some time of his plans to return home."
TNK-BP chief operating officer Tim Summers, one of the few senior foreign executives left at the company, praised Considine's contribution to the company.
"We regret we are losing Tony. ... He has set an outstanding example of cross-cultural performance and success," Summers said in the TNK-BP statement. "His team has embodied what TNK-BP was set up to achieve -- a unique and powerful blend of Russian and international expertise and talent."
Considine was a senior member of the TNK-BP Integration team managing the process of designing and structuring TNK-BP back in 2003, the company said in the statement.
"Prior to joining TNK-BP, he had previously enjoyed a successful international career with BP, working in a wide variety of senior commercial and management positions," the statement said.
In another development Monday, a lawyer for Dudley appealed the court's decision to disqualify his client from serving as TNK-BP's chief, Henshaw said. Dudley left Russia in July amid a work-permit dispute that he has linked to the shareholders feud.
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