"To know the man is to like the man," President Barack Obama said of his predecessor at the ceremony. "He is a good man."
Bush opened his own remarks with humor, joking that at one point in life he would never have been found in a library, much less have founded one.
He also responded to former-Presidents Jimmy Carter and Bill Clinton's praise for Bush's work in Africa.
"The political winds blow left and right, polls rise and fall, supporters come and go, but in the end, leaders are defined by the convictions they hold," Bush said at the library's ceremony. "My deepest conviction, the guiding principle of the administration, is that the United States of America must strive to expand the reach of freedom."
He went on to say that he knew the opening of the new presidential library in his name would reopen debates over the Iraq War and the policies he used in response to the September 11 terrorist attacks, but that he would stick by his convictions.
"A free society thrives when neighbors help neighbors and the strong protect the weak and public policies promote private compassion," said Bush. "As president, I tried to act on these principles every day. It wasn't always easy and certainly wasn't always popular ... but when future generations come to this library to study this administration, they're going to find out that we stayed true to our convictions."
At the end of his speech, Bush thanked his wife, parents, former aides, world leaders and his vice president, Dick Cheney, adding, "I'm proud to call you friend."