The deal is likely to pave way for the resumption of Rosneft's exports of fuel to Ukraine, which has faced with the prospects of diesel shortages.
The operations were halted after a ruling by Kiev's Supreme Anti-Corruption Court led to the seizure of diesel, owned by the Swiss-based trader, that was in the pipeline from Russia.
Rosneft's report said it would drill an exploration well in Myanmar, which has been rocked by protests since a military coup in February, at block EP-4, which the Russian oil firm inherited after it bought Bashneft in 2014.
Bashneft was one of several foreign companies awarded Production Sharing Contracts by Myanmar's government for 16 onshore energy blocks.