The deployment is aimed at showing solidarity with Ukraine and Britain's NATO allies.
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.
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.
Meanwhile, two Russian warships transited the Bosphorus en route to the Black Sea on Saturday and 15 smaller vessels completed a transfer to the sea as Moscow beefs up its naval presence at a time of tense relations with the West and Ukraine.
The reinforcement coincides with a huge build-up of Russian troops near Ukraine, something Moscow calls a temporary defensive exercise, and follows an escalation in fighting in eastern Ukraine between Russian-backed separatists and Ukrainian government forces.