Bush did not weigh in on immigration, instead welcoming former allies, including Vice President Dick Cheney, who appeared in a cowboy hat.
"There was a time in my life when I wasn't likely to be found in a library, much less found one," Bush joked.
But he said the library, and his presidency, would stand the test of time.
"When future generations come to study at this library, they're going to find out that we stayed true to our convictions," Bush said, and that he "made the tough decisions required to keep the American people safe."
Newly a grandfather, Bush showed no desire to return to public life, saying he hopes his center will press for his causes.
"I'm retired from politics — happily so, I might add — but not from service," he said, wiping away a tear and making a three-fingered "W" sign before leaving the stage.
In the audience, some wondered if the gesture signaled his support for Jeb Bush's candidacy — a potential third Bush in the White House.
Teresa Jimenez, 70, traveled to the event from Bridgeport, N.J., because she considers Bush "a man of heart." She said she would vote for his brother, too.
"He really loves this country, him and his family, and he does not brag about what he has done," said Jimenez, an obstetrician who emigrated from Cuba.
Cruz, who cut his teeth campaigning for Bush in 2000, said he learned from the president's example.
"His greatest strength was he did what he believed was right regardless of criticism and polls," Cruz said.
Many in Thursday's audience enjoyed seeing the camaraderie among presidents.
"There was such a positive spirit among the presidents, the friendships that have lasted through the years," said Diane West, a Dallas Republican who even found herself warming to Clinton, whose comments about immigration she said were timely.
"They made me laugh — I have tears in my eyes," said retired Houston Rockets center Dikembe Mutombo, who attended with former Dallas Maverick and Los Angeles Laker D.J. Mbenga. "It gives us a different impression. Sometimes we think of our former presidents in their own little rooms, not listening to each other."
Mutombo said he has teamed with all the presidents on humanitarian work in Africa, but it was George W. Bush who mentioned him during his 2007 State of the Union address. Mutombo, originally from Congo, said he appreciated Bush's efforts to fight AIDS in Africa and help broker peace in Sudan.
Annette Strake, a Bush family friend from Houston, praised the 43rd president's remarks at the opening. "I think it will inspire people — one of his best speeches ever," she said. Her husband, George Strake, former Texas secretary of state, called the celebration "a rare coming together of political philosophies."
But Stephen Boyd, 22, was bothered by Obama's mention of immigration, saying he should have "stuck with accolades." The SMU junior from nearby Richardson, Texas, was in fourth grade on Sept. 11, 2001, and came of age during the George W. Bush administration.
"He represents Texas to me, but as a nation, I think he represents real leadership," said the young Republican, who wore his black cowboy hat. "He was a steadfast leader: Once he decided something, he stuck to it. He's very much a statesman — I think he doesn't even know it now. You can see it in his improved ratings."
And how will history judge the 43rd president?
"That depends on who's writing it," Boyd said.
- The Latest: Defiant Kentucky clerk goes to...
- President Uchtdorf dedicates addition to...
- Kentucky clerks to license marriages as their...
- Trump vows no third-party bid, will back GOP...
- Gold fever hits Poland with possible...
- Disney unveils Star Wars toys amid marketing...
- Republican Huckabee to visit jailed Kentucky...
- FamilySearch opens new Seattle Family...
- Kentucky clerk still won't issue... 129
- The Latest: Defiant Kentucky clerk goes... 115
- Kentucky clerks to license marriages as... 81
- Compromise could fix Kentucky's wedding... 62
- Latest Clinton emails show frustrations... 26
- In Alaska, Obama depicts stark future... 21
- Obama gets Iran deal win as Senate Dems... 21
- AP sources: GOP seeks pledge to avert... 20