"Even though we knew this day was coming, we awaited it with no small amount of dread," Obama said.
"His extraordinary life on this Earth has come to an end. The extraordinary good that he did lives on."
Obama said Kennedy's ideas and ideals had been "stamped on scores of laws and reflected in millions of lives" as a result of his 47-year career in the US senate.
"He had been the voice of the voiceless and the defender of many defenceless people"
Obama's predecessor, former George Bush, also offered plaudits for Kennedy, noting that he had worked with the senator or a range of issues from immigration to public education.
"In a life filled with trials," Bush said, "Ted Kennedy never gave in to self-pity or despair."
Bush's father, former president George H.W. Bush, also added his tribute, noting that "while we didn't see eye to eye on many political issues through the years, I always respected his steadfast public service".
Nancy Regan, the widow of another Republican president, Ronald Reagan, called Kennedy "an ally and a dear friend".
"Ronnie and Ted could always find common ground, and they had great respect for one another," she said.
"In recent years, Ted and I found our common ground in stem cell research.''
Kennedy's political career saw him champion a range of causes including civil rights, universal health care, opposition to the war in Iraq and peace in Northern Ireland.
|Thousands across the US have paid their respects to Edward Kennedy [Reuters]
In Dublin Bertie Ahern, the Irish prime minister, paid tribute to the role Kennedy played as a key American powerbroker in the peace process that brought an end to years of violence in Northern Ireland.
"He lived to see two great chasms bridged, between Catholic and Protestant in Northern Ireland and between black and white in his own United States," Ahern said.
"These achievements, which were the dreams imagined by his brothers in his youth, were the legacy of a long life and of a good and great man."
At the UN headquarters in New York, Ban Ki-moon praised Kennedy for "keeping and upholding the ideals and goals of the United Nations", adding that his work "will be long remembered in the minds and in the hearts of many people, particularly vulnerable people, and those people whose human rights have been abused."
"He had been the voice of the voiceless and the defender of many defenceless people," the UN secretary-general told reporters.