It will also most likely be fitted with a new KRET defensive suite.
The new defensive suite might possibly have any combination of better infrared countermeasures, solid-state lasers, or beams of electromagnetic radiation to take out incoming missiles.
Source: The Drive, KRET
It will also reportedly have new avionics, sensors, and communications equipment.
It will reportedly have a new engine — four of the NK-32 02 series seen below — which will add 600 miles to its flying range.
The original engine on the Tu-160 — the NK-32 — is already a powerful engine, providing 55,000 lbs of thrust. The B-1B Lancer, on the other hand, only generates about 31,000 pounds of thrust.
Source: The Drive, The Aviationist
It's full capabilities are still unknown, but other than keeping the same frame, it will reportedly be a much different aircraft.
In 2015, Russian media reported that the new Blackjack would share 60% of its components with the older version.
You can find a full list of the original Tu-160's specifications here, and the Tu-160M modifications here.
Source: The National Interest
The Tu-160 is often compared to the US' B-1B Lancer.
Russia unveiled the new Tu-160M2 White Swan — codenamed Blackjack by NATO — on Thursday.