Kennedy after battling a brain tumor. He was 77.
In Britain and Ireland, he was remembered particularly for his involvement in the long process that led to Northern Ireland's 1998 Good Friday peace accord.
British Prime Minister Gordon Brown said that "even facing illness and death he never stopped fighting for the causes which were his life's work.
"He led the world in championing children's education and health care, and believed that every single child should have the chance to realize their potential to the full," Brown said.
Read more stories on Sen. Edward M. Kennedy's life and death:
"Liberal Lion" Remembered
No Immediate Action on Succession
In His Own Words
"The Last Brother"
Life in the Public's Glare
In Pictures: The Kennedys
Obits from U.S. Newspapers
Brothers "Would Have been Proud"
Former British Prime Minister Tony Blair called Kennedy "a true public servant committed to the values of fairness, justice and opportunity."
Britain gave Kennedy an honorary knighthood earlier this year.
Lord Owen, who served as British foreign secretary in the 1970s, said Kennedy was "the most influential senator" in the U.S.
He said Kennedy had put his weight behind peace in Northern Ireland even at the risk of alienating powerful Irish-American allies, whose sympathies lay with the province's Catholic Irish nationalists rather than the British Protestant majority.
"His influence on the peace process, and his influence on successive American presidents was I think absolutely crucial, and in particular of course on President (Bill) Clinton," Owen told the BBC.
Irish President Mary McAleese said Kennedy would be remembered "as a hugely important friend to this country during the very difficult times.
"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," she said.
Irish Prime Minister Brian Cowen said Kennedy had been "a great friend of Ireland.
"America has lost a great and respected statesman and Ireland has lost a long-standing and true friend," Cowen said.
In Australia, Prime Minister Kevin Rudd says Kennedy "made an extraordinary contribution to American politics, an extraordinary contribution to America's role in the world."
Italian President Giorgio Napolitano said in a statement that Kennedy "has left a deep mark and deserves the homage of all the free world."
Commentators also noted the passing of a political generation that included the late senator's assassinated brothers, President John F. Kennedy and Sen. Robert Kennedy.
"It is one of the strongest brands in American political history that withers away," said Michael Ehrenreich, editor-in-chief of Denmark's Kristeligt Dagblad newspaper and a leading expert on U.S. politics.