A source familiar with the situation said the additional payout for the first half of 2011 was approved at a board meeting in Cyprus on Friday.
“On top of $4.2bn already paid this year, it will bring total payments to $5.5bn,” the source said.
BP owns half of TNK-BP, and the other half is controlled by the Russia-connected consortium AAR.
BP stands to gain $625m in cash from the dividend payment, which has been granted in light of strong profit growth at TNK-BP.
The firm posted an 81 per cent jump in quarterly net profits to $2.11bn in July, on the back of surging oil prices.
The board is also understood to have rubber-stamped the acquisition of a 45 per cent stake in Brazilian oil exploration outfit Petra Energia, which was first announced in July.
The decisions were taken at the same meeting where Tony Hayward, former BP boss, formally resigned from the TNK-BP board after just short of a year in the job.
Hayward was forced out from BP in July 2010 in the wake of the Deepwater Horizon, in which 11 rig workers died and gallons of oil spilled into the Gulf of Mexico.
His departure from TNK-BP severs the last of his ties to BP, and frees up more time for him to work on the Vallares acquisition venture he set up with Nathaniel Rothschild.
The dividend can also be seen as a move to ease relations between the board’s various camps, following AAR’s sensational move to block BP’s joint venture with Russia’s Rosneft in January.
BP later dropped its $10bn share swap and exploration agreement with Rosneft, only to be replaced by Exxon in the lucrative deal.
However, BP is still fending off a lawsuit linked to the deal from minority shareholders in TNK-BP, who last week raised their claim to $4.9bn.
The TNK-BP board is made up of four BP representatives, including Hayward; four AAR representatives; and three independents, including former German Chancellor Gerhard Schroeder.
TNK-BP was unavailable for further comment last night. The company is expected to formally announce the results of its board meeting today.