France will fully refund Russia for the two helicopter carriers. The deal was worth €1.2bn (£838m; $1.3bn) and Russia made an advance payment of about €840m.
The Kremlin says that it now considers the dispute to be fully resolved.
French President Francois Hollande's office said that Russia will be "fully reimbursed" for the two warships.
It said that France will keep both vessels.
France stopped the planned sale after the outbreak of the conflict in eastern Ukraine.
The Kremlin said that France has agreed to pay back money Russia paid under the contract.
"France has already transferred these funds and, after the return of equipment, will acquire ownership and be able to take charge of both ships," it said in a statement.
The Elysee Palace statement said that all Russian equipment installed on the ships will be removed and handed back to Russia.
The deal was described last year as the biggest arms sale made by a Nato country to Russia.
The Mistral-class vessels carry about 700 troops, 16 helicopter gunships and up to 50 armoured vehicles.
Last month President Hollande denied claims that a deal had been reached. At that time it was suggested that France would compensate Russia to the tune of €1.16bn.
That sum included the amount that Russia has already spent on special training for 400 sailors, on port infrastructure in Vladivostok for the two warships and on developing four prototype Ка-52К helicopters.
Western sanctions have been ratcheted up against Russia since March 2014, when Russia annexed the Ukrainian region of Crimea.
Russia denies backing pro-Russian separatist rebels fighting in eastern Ukraine.
A deal has been agreed in which Russia will receive compensation for France's decision last year to cancel the sale of two warships, both countries say.