In 2011, relations worsened when BP tried to strike a separate partnership with Rosneft to explore for oil beneath the Arctic Ocean. AAR subsequently sued and got the deal blocked, alarming BP investors.
Dudley said in the statement Monday that "BP intends to be a long-term investor in Rosneft -- an investment which I believe will deliver value for our shareholders over the next decade and beyond."
Ildar Davletshin, an oil and gas analyst at Renaissance Capital, said the deal "strategically looks very positive for BP," which has replaced "a private partner for a strategic national company which has much bigger access to resources in Russia and has much bigger political support in this country."
Davletshin added that Rosneft will more likely be run "in the interests of shareholders" rather than serving the Kremlin's political agenda since BP will have two board members. Rosneft has been involved in an array of overseas projects largely viewed as unprofitable but designed to prop up the Kremlin's foreign policy.
Sechin sounded optimistic about their tie-up with BP, saying that his company "would benefit from BP's experience and its track record of implementing best international practices in Russia."
Rosneft shares jumped more than 3 percent on the announcement but rolled back to trade only 1.6 percent higher at 218 rubles per share.
BP shares were up 0.57 percent to 453 pence following the announcement.
Ratings agency Fitch last week warned Rosneft of a possible rating downgrade because of the TNK-BP deal. Fitch said the Russian company should have no problems raising the money to pay for 50 percent, but said the purchase of the other 50 percent could require so much borrowing that it could lead to a downgrade.
Barr reported from London; Laura Mills contributed to this report from Moscow.