"We are delighted to close this transaction ahead of schedule and would like to thank our partners in BP for their cooperation throughout the process," Rosneft President and Chairman of the Management Board Igor Sechin said in a statement.
Rosneft said it paid $28 billion for the 50 percent stake in TNK-BP held by AAR. This year, the state-owned oil company reached a deal with BP to buy its half of TNK-BP for more than $17 billion in cash.
Early this month, the European Commission cleared the way for the acquisition, saying it didn't raise competition concerns "because the merged entity would continue to face constraints from a number of strong competitors."
BP Chief Executive Bob Dudley said the deal was "historic" for his company's role in Russia, where BP aims to exploit arctic reserves.
Dudley left TNK-BP in 2008 during disagreements over the company's direction. TNK-BP later expressed frustration over a failed 2011 proposal with Rosneft to work in the arctic, accusing BP of violating terms of the shareholder agreement with BP.
Rosneft now stands beside supermajors such as Chevron and Royal Dutch Shell in terms of crude oil production.