The Fort Victoria and its tracking helicopter were charged with intercepting a suspected pirate vessel the day after the USS Carney first discovered and tracked the Somali pirate ship, NATO officials said in a release.
NATO did not release the number of pirates who surrendered.
NATO officials said the helicopter had to fire several warning shots before a Royal Marines boarding team approached the vessel and boarded it successfully. Soon after the Marines approached, the pirates surrendered and moved to the front of the boat with their hands raised.
Officials said a search of the pirate vessel uncovered many weapons, including rocket-propelled grenade launchers and machine guns.
On Thursday, six Somali pirates were arrested after trying to hijack the flagship of a European Union force patrolling waters near the Horn of Africa, officials said.
The EU's anti-piracy command said the pirates opened fire before trying to board the Spanish warship Patino from a skiff but then tried to flee when the ship's crew returned fire, the British newspaper The Daily Telegraph reported.
The attack on the 17,000-ton vessel occurred after the Patino finished escorting a cargo ship carrying famine food aid to Somalia's capital of Mogadishu, officials said.
"The suspected pirates opened fire with light-caliber weapons and tried to board the Patino," the anti-piracy force command said in a statement. "The ship's force-protection team returned fire in self-defense and the ship's helicopter was launched. The skiff broke off the attack and the men surrendered to the helicopter after throwing their weapons, ladder and fuel barrels overboard."