The deployment is aimed at showing solidarity with Ukraine and Britain's NATO allies, the newspaper reported.
One Type 45 destroyer armed with anti-aircraft missiles and an anti-submarine Type 23 frigate will leave the Royal Navy's carrier task group in the Mediterranean and head through the Bosphorus into the Black Sea, according to the report.
RAF F-35B Lightning stealth jets and Merlin submarine-hunting helicopters will stand ready on the task group's flag ship, the carrier HMS Queen Elizabeth, to support the warships in the Black Sea, the report added.
A spokesman for the UK Ministry of Defence told the newspaper that the UK government was working closely with Ukraine to monitor the situation and continued to call on Russia to de-escalate.
"The UK and our international allies are unwavering in our support for Ukraine's sovereignty and territorial integrity", the newspaper quoted the spokesman as saying.
As reported earlier, the US, alarmed by the military buildup in eastern Ukraine and Russia’s moving warships and landing craft from the Caspian Sea to the Black Sea, said it was sending two warships to the Black Sea, and Russia had warned the US to stand down. As a result, the ships were turned around on April 14 following the Russian warnings.