The Prince of Wales led a two-minute silence at the National Memorial Arboretum in Staffordshire, as part of a service of remembrance.
Later, in a TV address, his elder son Prince William urged the public "to learn the lessons of the past".
And a message from the Queen thanked those "who fought so valiantly".
She said: "Those of us who remember the conclusion of the Far East campaign, whether on active service overseas, or waiting for news at home, will never forget the jubilant scenes and overwhelming sense of relief."
The Prince of Wales attended the event at the arboretum with the Duchess of Cornwall.
He laid a wreath at the Kwai Railway Memorial, as a small number of veterans and their relatives sat on benches dotted around the garden, to maintain social distancing.
A Battle of Britain Memorial Flight flypast also commemorated those who fought.
In a speech, Prince Charles said the veterans' service "will echo through the ages."
He referred to the description of them as the Forgotten Army, noting how many soldiers, nurses and other personnel felt aggrieved at the way some of the public associated the end of World War Two with the victory in Europe in May 1945.
"Let us affirm, they and serving veterans are not forgotten, rather you are respected, thanked and cherished with all our hearts and for all time," he said.
Prime Minister Boris Johnson, who also attended and read the poem The Exhortation before the silence, thanked those who had fought for restoring "peace and prosperity".
In a pre-recorded speech for BBC One's VJ Day 75: The Nation's Tribute - broadcast on Saturday evening - the Duke of Cambridge spoke of how King George VI addressed the nation on August 15 1945 as "the most catastrophic conflict in mankind's history came to an end".
"It is hard for us to imagine what Victory over Japan Day must have felt like at the time; a mix of happiness, jubilation, and sheer relief, together with a deep sadness and overwhelming sense of loss for those who would never return home.
"Today we remember those who endured terrible suffering and honour all those who lost their lives."
He cautioned: "As we look back, we must not forget our responsibility to learn the lessons of the past and ensure that the horrors of the Second World War are never repeated.
"We owe that to our veterans, to their families, and to the generations who will come after us.
He went on to thank those veterans, among them his own grandfather, the Duke of Edinburgh, who "remembers vividly his role in collecting released prisoners of war", said Prince William.
Prince Philip was a young Royal Navy officer aboard a warship in Tokyo Bay when Japan surrendered.
As part of the commemorations, he appeared in a photo montage of veterans which featured on large screens in locations across the country throughout the day. In the montage each veteran was pictured with an image of themselves from their time in service.
It marked a rare appearance for Prince Philip, 99, who has only been seen a handful of times in public since retiring in 2017 - most recently for a military event at Windsor Castle.
Earlier in the morning, Defence Secretary Ben Wallace was joined by military chiefs as he placed a wreath at the Cenotaph in London.
The defence secretary also met some of the famous Chelsea Pensioners during his visit to their iconic home, the Royal Hospital Chelsea, as part of events to mark the 75th anniversary.
But the Red Arrows - who were due to carry out a flypast over the capital cities of all four nations of the UK - were forced to cancel flights over Edinburgh, Cardiff and London, where they were to fly directly over the Royal Hospital Chelsea, due to poor weather conditions.
They were, at least, able to fly over Belfast, and pilots met three veterans during a stop at Prestwick, near Glasgow.
VJ Day - or Victory over Japan Day - on 15 August 1945 ended one of the worst episodes in British military history, during which tens of thousands of servicemen were forced to endure the brutalities of prisoner of war camps.
It is estimated that there were 71,000 British and Commonwealth casualties of the war against Japan, including more than 12,000 prisoners of war who died in Japanese captivity. More than 2.5 million Japanese military personnel and civilians are believed to have died over the course of the conflict.
The fighting in Europe had ended in May 1945, but many Allied servicemen were still fighting against Japan in east Asia.
Japan rejected an ultimatum for peace, and the US believed that dropping a nuclear bomb would force them to surrender. The US dropped two atomic bombs on Japan, killing an estimated 214,000 people, and two weeks later Japan surrendered.
To mark the 75th anniversary, Japan's Prime Minister Shinzo Abe sent an offering to a controversial war shrine in Tokyo, but did not attend in person.
However, two of his ministers did visit the Yasukuni Shrine, in which 14 leaders who were later convicted by the Allies as war criminals are commemorated.
The National Memorial Arboretum seems to lend itself perfectly to the concept of a socially distanced commemorative service.
Veterans of the Burma campaign, their families, and other guests sat on chairs spaced out on the grass between the trees.
The proceedings focused on the multinational and multicultural make up of the Allied forces that fought the Japanese.
Gurkhas, alongside Sikhs, sat next to troops from Welsh and Scottish regiments, representing the 40 nations involved in the Far East.
After sitar music, readings from British Asian actors, and speeches from descendants of those who fought, the roar of aircraft engines could be heard overhead. A Lancaster, Hurricane and three Spitfires from the Battle of Britain Memorial flew over in formation and in tribute.
Then those who could stand, were invited to do so for a two-minute silence.
The Prince of Wales then laid a wreath at the Burma Railway Memorial.
Flowers had been placed between the sleepers and track that make up the memorial. It was known as the "Death Railway" and 16,000 prisoners of war died during its construction.
It makes an incongruous, yet incredibly poignant sight among the granite and brass of the other memorials.
Boris Johnson earlier joined other world leaders including US President Donald Trump in recording a video message to thank veterans.
In the video, each leader says in turn: "To all who served, we thank you."
Mr Johnson added: "On this 75th anniversary of the end of the Second World War, we pay tribute to the heroes deployed thousands of miles away in the mountains, islands and rainforests of Asia.
"Unable to celebrate the victory in Europe, and among the last to return home, today we recognise the bravery and ingenuity of those who, in the face of adversity, restored peace and prosperity to the world.
"Their immeasurable sacrifice changed the course of history and, at today's commemorations, we take the opportunity to say what should be said every day - thank you."
In a letter specifically addressed to Far East veterans, Mr Johnson said: "You were the last to come home but your achievements are written in the lights of the glittering capitals of the dynamic region we see today."
"All of us who were born after you have benefitted from your courage in adversity. On this anniversary, and every day hereafter, you will be remembered," he added.
Labour leader Sir Keir Starmer also recorded a message, paying tribute "to the wartime generation, who through the horrors of conflict showed us the spirit and determination that we need to always remember and always be grateful for".
"It's important that as we face the challenges of today, we take inspiration from that generation," he said.
Meanwhile Capt Sir Tom Moore, who served in the Burma campaign has encouraged the public to join in the commemorations, describing VJ Day as "the most special day".
"It was VJ Day when the pain of war could finally start to fall away as peace was declared on all fronts," said Sir Tom - who raised millions of pounds for NHS charities by walking laps of his garden during lockdown.
"I respectfully ask Britain to stop whatever it is doing and take some time to remember.
"We must all take the time to stop, think and be thankful that were it not for the ultimate sacrifices made all those years ago by such a brave band of men and women, we would not be enjoying the freedoms we have today, even in these current difficult times."
The question isn't who is going to let me; it's who is going to stop me.