A start date for the one-year trial scheme "will be announced soon", the Global New Light of Myanmar reported, citing the junta's immigration ministry.
Holders of the visas will be "allowed to visit all sites apart from restricted areas for security concerns", said the report in Thursday's newspaper.
Currently citizens of both countries must apply for a tourist visa online, or at a Myanmar embassy.
Earlier this month the national carrier began direct flights to Russia's Novosibirsk, and the junta has said it is working to allow the use of Russia's Mir cards for direct payments.
Myanmar opened up to tourists in 2011 following decades of military rule, becoming popular with travelers.