MOSCOW — BP’s board has approved an offer from the Russian state oil company, Rosneft, to buy most of BP’s business in Russia for cash and shares in Rosneft, further consolidating Russia’s control of its oil industry, an executive with knowledge of the decision said.

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 Putin. Later, BP is hoping to use this new strategic tie with the Kremlin to drum up other business.