The sale was approved by Russian Prime Minister Dmitry Medvedev on Monday, according to reports in the Russian press.
The deal for just over 50% of Bashneftis reportedly expected to be closed by 14 October.
The acquisition follows plans of the Russian Economy Minister Alexei Ulyukayev announced earlier this year to privatise a stake in Bashneft.
The agreed sale, however, came as a surprise as initially the government said it should delay selling its stake for up to five years, until the company was worth more.
Bashneft