The fate of the ships has plagued Franco-Russian ties for months following Paris' decision in November to put the USD 1.3-billion deal on ice as the West slapped sanctions on Moscow over its annexation of Crimea and alleged backing of rebels in Ukraine.
The French presidency said in a statement that Russia would be "fully reimbursed" for the two helicopter carriers, which France will keep.
It added that all Russian equipment installed on the ships will be removed and handed back to Russia.
"The president of Russia and the president of France took a joint decision to annul the contract. Moscow considers the Mistral issue to be completely settled," the Kremlin said in a statement after a phone talk between the two leaders.
A Russian military source had yesterday told state-run news agency TASS that a group of Russian specialists will be sent to France in September to dismantle and return communication equipment already onboard the ship.
The first ship had been due for delivery in 2014, while the second was to be delivered this year.
In June last year, US President Barack Obama had urged Paris to "press the pause button" on its deal with Russia, signed in 2011.
The EU and US have slapped damaging sanctions on Moscow, and while there have been repeated attempts to negotiate an end to clashes between Kiev and the pro-Russian rebels in the east, none have held out.
Earlier this year, Hollande said that the conditions for delivery of the ships were "still not right".
In April, Putin downplayed the importance of the ships but insisted that the French side reimburse Moscow "all expenses" if the contract were to be terminated.
