An estimated 30,000 guests were on hand for the dedication of the $165 million glass-and-steel home of artifacts and documents gathered during Mr. Clinton's eight years in the White House.
All the living presidents except Gerald Ford were on stage during the dedication ceremony under rainy skies in Little Rock, Ark.
President Bush praised the skills Mr. Clinton demonstrated in office.
"Over the years, Bill Clinton showed himself to be much more than a good politician. ... He was an innovator, a serious student of policy and a man of compassion," the current president said.
Former President George H.W. Bush, whom Mr. Clinton defeated in 1992, noted his campaign skill and added, "And, oh, how I hated that."
Former President Carter admired Mr. Clinton for his "insight, wisdom and determination."
"He was a leader who could inspire other people to go beyond what they thought were their own limits in accomplishing great goals," Mr. Carter said.
Mr. Clinton, still recovering from his September cardiac surgery, often chuckled and slapped his thigh during the remarks. He sported a new hairstyle, parted on the side instead of swept back.
U2's Bono and The Edge played the Beatles song "Rain" and
"I believe the job of a president is to understand and explain the time in which he serves, to set forth a vision of where we need to go and a strategy of how to get there, and then to pursue it with all his mind and heart," he told the crowd.
Mr. Clinton paid tribute to the people of Arkansas, his family, his predecessors and his colleagues, and he said he tried to combine the best of conservatism, maintaining what is worth keeping, and progressivism.
The collection consists of more than 80 million presidential items, and Mr. Clinton has promised to give scholars early access to previously private policy advice and other documents he isn't required to release until 2006.
Wet bleachers and lengthy security lines earlier in the day did little to squelch the enthusiasm of thousands waiting to attend. Sister Judith Dalesandro was among four nuns who arrived from a Roman Catholic convent in Jonesboro.
"Bill Clinton is the best president we've ever had in the United States," said Sister Dalesandro, who taught school in Little Rock when Clinton was Arkansas governor. "He was wonderful. He wasn't at all snooty. He would come and talk with the kids."
When the building opens to the public Friday, visitors paying $7 can peruse the library's 14 alcoves detailing aspects of Mr. Clinton's Oval Office years — one of which is dedicated to scandal.
"It's just been an overwhelming experience to actually see the library after all of the work. Bill has poured his heart into this labor of love," Hillary Rodham Clinton told CBS News Early Show Co-anchor Harry Smith. "The exhibits are an incredible walk down memory lane. It's a full and comprehensive picture of those eight years for us and for the nation."
A presidential timeline opens with Mr. Clinton's 1993 inaugural address and his dream for the nation: "There is nothing wrong with America that cannot be cured by what is right with America."
Eight 18-foot-wide panels offer highlights and lowlights from each year of the Clinton presidency, such as the Oklahoma City bombing, Clinton-led peace efforts in Northern Ireland and the Middle East, and Mr. Clinton's impeachment and acquittal over the Monica Lewinsky affair.
The Lewinsky matter is covered in an alcove dedicated to the "politics of persecution." The display lumps together Newt Gingrich's "Contract With America" and independent counsel Kenneth Starr's Whitewater investigation.
Library director David Alsobrook acknowledged that many wouldn't be satisfied.
"His supporters will say, 'Oh, why did you give this so much space?"' Alsobrook said as reporters received advance tours Wednesday. "But his detractors will come up and say, `Dave, where is the blue dress?"'
Another feature is the only full-scale replica of the Oval Office in a presidential library. Administration officials took thousands of photographs of the office to re-create the placement of every statue, photo and award.
Mr. Clinton said the library contained the essence of his presidency.
"The record is all in there — what we did at home, and what we did abroad. ... Even when we fell short, we pushed ahead," he said.