According to Lt-General Viktor Bondarev, the Commander of the Russian Air Forces, the new strategic bomber, currently known as PAK DA, is expected to made its first flight in 2019 and to begin service in 2023.
The contract to develop the new bomber was signed with the Tupolev design bureau in February 2014. The preliminary R&D was reported to begin earlier, in 2011. At the time it was expected that the aircraft will be ready for deployment in 2025.
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Tests of the PAK DA engine prototype began:
http://www.kuznetsov-motors.ru/press-center/news/oao-%C2%ABkuznetsov%C2%BB-usilivaet-konstruktorskii-potentsial-v-oblasti-sozdaniya-aviatsion