"The purpose of public office is not to fulfill personal ambitions; elected officials must serve a cause greater than themselves," Bush told an audience that included U.S. and foreign dignitaries, family and friends.
The dedication of the 13th presidential library took place under sunny skies Thursday on the Southern Methodist University campus in Dallas.
"In the end, leaders are defined by convictions they hold. My deepest conviction ... is that the United States of America must strive to expand the reach of freedom," he said. "I believe freedom is a gift from God and the hope of every human heart."
"I dedicate this library with unshakable faith in future of this country," Bush said.
His voice quivering, Bush said he had "the honor of a lifetime to lead a country as brave and as noble as the United States. Whatever challenges come before us, I will always believe our nation's best days lie ahead. God bless."
Bush thanked his "fellow members of the former presidents club" and for the examples they set.
He singled out his father, President George H.W. Bush, beset by illness in recent months and who attended the ceremony in a wheelchair.
"Bush 41, it is awesome that you are here today," the son told the father and giving his presidential number.
President Obama spoke of how Bush left a letter that demonstrated his "compassion and generosity."
In the letter, Bush said he knew that Obama "would come to learn what he had learned -- that being president, above all, is a humbling job."
Recalling former President Bill Clinton's remarks about Bush, Obama said, "To know the man is to like the man because he's comfortable in his own skin. ... He takes his job seriously but he doesn't take himself seriously. He is a good man."
Obama, Clinton and President Jimmy Carter all praised Bush's efforts in immigration, providing financial and humanitarian assistance to African countries and other issues.
"I like President Bush. He's disarmingly direct," Clinton said of his successor, with whom he worked in Haiti following an earthquake in January 2011, and which George H.W. Bush on several humanitarian projects.
"Each library is about our nation and the world during our time" in office, former first lady Laura Bush said. "Here we remember the heartbreak and heroism of Sept. 11. We remember volunteers of all ages who came to the Gulf Coast following Hurricane Katrina ..."
The library will be open to the public next Wednesday.
It includes girders from the World Trade Center towers felled on Sept. 11, 2001, as well as the bullhorn Bush used to speak to first responders at Ground Zero.
Museum Director Alan Lowe told C-SPAN the library holds more than 70 million pages of paper records from Bush's administration, more than 80 terabytes, including 200,000 email messages, and 42,000 artifacts, as well as a range of audio/video artifacts.
The Bush library is the largest and most expensive presidential library, NBC News said. The library has 226,560 square feet and carries a price tag of $250 million. It was designed by Robert A.M. Stern, the dean of architecture at Yale University, Bush's alma mater.