Under the terms of the deal, BP would remain in Russia but — initially at least — only as a minority investor in an oil company controlled by the government of President Vladimir V. Putin. Later, BP is hoping to use this new strategic tie with the Kremlin to drum up other business.

BP had been telegraphing its willingness to make a deal for some time, and Rosneft formally submitted an offer on Thursday to buy out BP’s 50 percent of a joint venture here called TNK-BP.

The board’s authorization allowed BP’s chief executive, Robert W. Dudley, to negotiate the final terms for BP’s sale of its Russian holdings within a range of acceptable combinations of cash and shares, the executive with knowledge of the decision said.

The ranges were $10 billion to $14 billion and 15 to 20 percent of Rosneft’s shares. BP is likely to receive at least one seat on the board.

A formal announcement is expected as early as Monday. BP’s stock rose about 4 percent last week when it became clear that a deal was imminent.

For BP, the sale comes as the biggest step yet in Mr. Dudley’s “shrink to grow” strategy in the wake of the 2010 Gulf of Mexico oil spill.

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