Boris Johnson joined veterans, bereaved family members and senior defence figures at a service at Staffordshire's National Memorial Arboretum. Mr Johnson praised the "incredible daring and bravery" of Falklands veterans.
Some 255 British troops, 649 Argentine military personnel and three Falkland islanders died during the conflict.
The 10-week war began in April 1982, when troops from Argentina invaded the Falkland Islands, a British colony in the south Atlantic ocean.
Argentina said it had inherited the islands from Spain in the 1800s and wanted to reclaim them. The British had ruled the islands for 150 years and sent armed forces by sea to take the islands back. Argentina's troops surrendered on 14 June.
On Tuesday, veterans, civilians and bereaved family members attended a service hosted by the Royal British Legion at the National Memorial Arboretum in Alrewas to remember the end of the conflict. At the same time a service was held at Port Stanley, the Falklands capital.
Mr Johnson - who laid a wreath at the service - told journalists afterwards: "The first thing is to remember what an incredible thing it was that they achieved back in 1982 to make an opposed landing, to take back territory in the way that they did.
"The incredible daring and bravery of those young men and women. And we salute that - we remember that today."
He added that the "greatest tribute" to those who had laid down their lives was that the Falklands Islands had since "thrived in peace and freedom".
The city of Stanley on the Falkland Islands struck a sombre tone on Tuesday's morning under a grey winter drizzle.
Hundreds turned out to watch the band parade along the harbour front to the city's monument, where islanders paid their respects and to those who lost their lives in the conflict 40 years ago.
Soon after the memorial was over, the mood changed to celebration.
This is a defiant nation and one that wants the world to know it takes its freedom seriously, not taking a moment of it for granted.
The festivities will continue long into the night, a momentary breath of fresh air away from the dark cloud that continues to hang over these islands 40 years on, that of Argentina.
SOURCE:BBC
