"I have personally benefited and grown from his experience and advice, and I know countless others have as well," the governor said in a statement. "Teddy taught us all that public service isn't a hobby or even an occupation, but a way of life and his legacy will live on."
Kennedy's death came just two weeks after that of Shriver's mother, Eunice Kennedy Shriver, one of the senator's siblings.
Former Massachusetts Gov. Mitt Romney, a 2008 GOP presidential contender, recalled losing to Kennedy in a Senate race.
Nonetheless, the two joined forces in 2006 to help pass a universal health insurance law in Massachusetts.
"In 1994, I joined the long list of those who ran against Ted and came up short. But he was the kind of man you could like even if he was your adversary," Romney said.
The Senate's top Democrat, Sen. Harry Reid, D-Nev., labeled Kennedy the "patriarch" of the party.
The Senate majority leader promised that Congress, while mourning Kennedy's loss, would renew the push for the cause of Kennedy's life -- health care reform.
"Ted Kennedy's dream was the one for which the founding fathers fought and for which his brothers sought to realize," Reid said in a statement. "The liberal lion's mighty roar may now fall silent, but his dream shall never die."
Former President Jimmy Carter, who beat out Kennedy for the 1980 Democratic presidential nomination, called him "an unwavering advocate for the millions of less fortunate in our country."
"The courage and dignity he exhibited in his fight with cancer was surpassed only by his lifelong commitment and service to his country," Carter said in a statement.
Kennedy's junior colleague, Sen. John Kerry, D-Mass., lauded him for his cancer fight.
"He taught us how to fight, how to laugh, how to treat each other, and how to turn idealism into action, and in these last fourteen months, he taught us much more about how to live life, sailing into the wind one last time," Kerry said.
"No words can ever do justice to this irrepressible, larger than life presence who was simply the best -- the best senator, the best advocate you could ever hope for, the best colleague and the best person to stand by your side in the toughest of times."
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