STORY: British Prime Minister Boris Johnson marked the occasion at the National Memorial Arboretum in Staffordshire.
Johnson met with veterans before the service and paid tribute to the "incredible achievement" of the armed forces.
British Foreign Secretary Liz Truss in a video message paid tribute to the efforts and sacrifice of the service men and women.
Britain had controlled the islands, about 300 miles (480 km) off the southern Argentine coast, since 1833 and refused to negotiate with Argentina over its claim of sovereignty over the territory.
The war began when Argentine troops landed on the islands on April 2, 1982, and ended 74 days later with their surrender.
During the conflict more than 900 people lost their lives, including approximately 650 Argentine and 255 British troops, and three Falkland Islanders.