Mr Brown praised the senator for "fighting for the causes which were his life's work" even as he faced illness and death.
Politicians lined up to pay tribute to Mr Kennedy following the announcement from his family today that the 77-year-old senator, who was diagnosed with a malignant brain tumour last year, had died.
Mr Brown said: "Senator Edward Kennedy will be mourned not just in America but in every continent.
"He is admired around the world as the senator of senators.
"He led the world in championing children's education and health care, and believed that every single child should have the chance to realise their potential to the full.
"Even facing illness and death,, he never stopped fighting for the causes which were his life's work.
"I am proud to have counted him as a friend and proud that the United Kingdom recognised his service earlier this year with the award of an honorary knighthood."
He added: "My thoughts and those of Sarah are with his remarkable and loving wife Vicki and his great family."
Mr Kennedy made the single greatest contribution of any American to helping resolve the Northern Ireland problem according to one prominent Ulster politician.
Alex Attwood, a Social Democratic and Labour Party member of the Stormont Assembly, said: "I think his death is a great loss."
The West Belfast MLA added: "He made a huge contribution to the North, the single greatest contribution of any American politician of recent times - including Clinton."
He said he had been fortunate to have met Senator Kennedy twice, most recently in 2005.
"The last time he was already failed but he still had a grasp of what was going on in Ireland, and not just broad brush strokes.
"He was all of the things you expected a Kennedy to be, he had great charm and enormous insight."
Senator Kennedy was seen as leaning towards republicansism on the Northern Ireland issue early in the troubles and constantly called for British troops to be removed.
But he later modified his stance and in 2005 he publicly snubbed Sinn Fein President Gerry Adams by cancelling a previously arranged meeting.
The Rev Ian Paisley, who had long vilified him, even paid tribute to his contribution to the negotiations which led to the Good Friday Agreement and the establishment of the devolved power-sharing administration at Stormont.
In December 2007 he met Mr Paisley, by then Northern Ireland First Minister, and Martin McGuinness, the Deputy First Minister, during their first joint visit to the US - a visit he said had been a great success.
The Senator for Massachusetts since 1962 was awarded his honorary Knighthood earlier this year for "services to British- American repationships and to Northern Ireland."
Proposing Mr Kennedy for the Knighthood Prime Minister Gordon Brown said: "Northern Ireland is today at peace, more Americans have health care, more children around the world are going to school and for all those things we owe a great debt to the life and courage of Senator Edward Kennedy."
Former prime minister Tony Blair added his tribute, praising his "passionate commitment" to the Northern Ireland peace process.
He said "Senator Kennedy was a figure who inspired admiration, respect and devotion, not just in America but around the world.
"He was a true public servant committed to the values of fairness, justice and opportunity.
"I saw his focus and determination first hand in Northern Ireland where his passionate commitment was matched with a practical understanding of what needed to be done to bring about peace and to sustain it.
"I was delighted he could join us in Belfast the day devolved government was restored.
"My thoughts and prayers today are with all his family and friends as they reflect on the loss of a great and good man."
Mr Kennedy was famous as much for his own achievements as for the legendary family he belonged to.
But it was a political dynasty that was cursed by tragedy.
Two of Edward Kennedy's brothers were assassinated in the 1960s. President John F Kennedy was gunned down in Dallas in 1963 and senator Robert F Kennedy was killed in Los Angeles as he campaigned for the 1968 Democratic presidential nomination.
Edward Kennedy's own hopes of reaching the White House were damaged in 1969 by a scandal that came to be known as Chappaquiddick.
He drove his car off a bridge and into a pond on Chappaquiddick Island, Massachusetts. Mary Jo Kopechne, 28, was found dead in the submerged car's back seat 10 hours later.
Mr Kennedy, then 37, pleaded guilty to leaving the scene of an accident and received a two-month suspended sentence and a year's probation.
But despite the incident tainting his career, he went on to become a dominant voice on health care, civil rights, war and peace, and more.
He was elected to the Senate in 1962, when his brother John was president, and served longer than all but two senators in history.
Northern Ireland Secretary Shaun Woodward said he was "deeply saddened" to hear of the death of Mr Kennedy.
Mr Woodward said; "Ted Kennedy was a true and constant friend of the peace process in Northern Ireland whose huge influence in engaging the United States in that process cannot be over-estimated.
"In every sense he was an immense figure whose part in transforming Northern Ireland will be a lasting memorial.
"My thoughts are with the Kennedy family today."
In Ireland, Taoiseach Brian Cowen said Mr Kennedy will be remembered with great affection.
Mr Cowen described Mr Kennedy as one of the most distinguished and talented figures in American politics.
He said: "Throughout his long and distinguished career in politics, Ted Kennedy has been a great friend of Ireland.
"He has used his considerable influence in the world's most powerful parliament for the betterment of this island.
"In good days and bad, Ted Kennedy worked valiantly for the cause of peace on this island."
Tory leader David Cameron said: "I was saddened to learn of the death of Senator Kennedy.
"During his life he served the American people in the spirit of a family whose name is synonymous with public service in the United States.
"He fought for the causes he stood for, from civil rights to education and healthcare.
"He bore his illness with great courage and dignity, and remained active in politics until the very last days of his life.
"He should be remembered as one of the most effective legislators in the history of the US Senate, a symbol of the strength and independence of the United States legislature."
Irish President Mary McAleese said Mr Kennedy would be remembered as a politician who had a deep connection with the needs of ordinary people.
"He will be remembered here in Ireland as a hugely important friend to this country during the very difficult times," she said.
"His death will be greeted with a great sense of sadness here because of his long-standing affection for this country, not just with the peace process, but on many other issues, including emigration.
"His outstanding and remarkable personal contribution was made, despite the sacrifice and sorrow that was part of the overall contribution of the entire Kennedy family."
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