Pirates had exchanged gunfire with a super tanker on Friday 11 October before attacking a Spanish fishing vessel three days later.
Combined Maritime Forces (CMF) traced the pirates' skiffs from Britain's Royal Fleet Auxiliary Fort Victoria.
Nine men were caught and forces later destroyed two boats and equipment.
Commodore Jeremy Blunden, Royal Navy, Commander of CTF-151, said: "This is an excellent result.
"My multinational counter piracy forces swiftly located and dealt with this Somali pirate group, sending a clear message that piracy no longer pays."
Combined Task Force (CTF) 151, as the group is known, embarked on board RFA Fort Victoria with support from Australian guided-missile frigate HMAS Melbourne and South Korean destroyer ROKS Wang Geon.
The European Union flagship Dutch HNLMS Johan de Witt - flagship of the EU naval force in the area - and maritime patrol aircraft from Luxembourg were also part of the mission.
After tracing the pirates an HMAS Melbourne Seahawk guided the warship to their precise location,  500 nautical miles off the Somali coast, before a boarding team made the final approach to search the skiffs.
Commander Brian Schlegel, Royal Australian Navy, commanded HMAS Melbourne during the operation.
He said: "It is clear that there are still pirates out there determined to generate income from taking merchant ships hostage.
"Mariners have been served a timely reminder of the perils of transiting the Somali coastline."
CMF is a multinational naval partnership with 29 nation members. Its aim is to promotes security, stability and prosperity across 2.5 million square miles of international waters.
A counter-piracy task force commanded by a Royal Navy officer has caught a group of Somalis believed responsible for two attacks in the Indian Ocean.