At a joint news conference, Rigali called Chaput a "fearless" proclaimer of the Gospel and said, "This is a new moment in the life of this local church."
"I'm happy to be in Philadelphia," said Chaput, adding later, "I do not know why the Holy Father sent me."
Referring indirectly to the sexual abuse scandal, he said of himself: "No bishop will try harder to help persons who have been hurt by the sins of the past or work harder to strengthen or encourage our priests and to renew the hearts of our people."
Earlier today, Pope Benedict XVI announced he had accepted Rigali's resignation and named Chaput, now archbishop of Denver, as his successor.
The two later celebrated mass together at the Cathedral Basilica of Saints Peter and Paul.
Chaput, 66, will be installed in the cathedral on Sept. 8, the feast of the birth of the Blessed Virgin Mary.
The pope has appointed Rigali as Apostolic Administrator with all of the responsibilities of archbishop until the Chaput's installation.
In his remarks, Rigali announced he would be spending his retirement in Knoxville, Tenn.
Chaput, who becomes Philadelphia's 13th bishop and ninth archbishop, was ordained a priest in 1970 and became a bishop at the age of 43. He was bishop of Rapid City, S.D., before becoming archbishop of Denver in 1997.
A Franciscan priest of the Capuchin order, Chaput (pronounced shap-you) was the first American Indian to become a Roman Catholic archbishop when he was named to Denver in 1997. His mother's family belongs to the Potawatomi tribe, and he was made a member as a boy.
Under Canon law, Rigali, archbishop since October 2003, submitted his resignation when he turned 75 in April 2010.
It is common for a bishop to continue serving until the pope names a successor and Rigali stressed again today that his resignation was pro forma and not related to the troubles bedeviling the archdiocese.
There are 1.5-million Roman Catholics in the Archdiocese of Philadelphia, which also includes Bucks, Montgomery, Chester and Delaware counties.
Admirers and critics alike describe the outspoken Chaput, 66, as a politically attuned and emphatically conservative champion of Catholic values who will seek to reenergize Catholic identity here.
Although Rigali has been struggling since February with the Philadelphia grand jury report that excoriated the archdiocese for harboring sexually abusive priests, his retirement was long expected this year.
Some Catholics said Monday it was appropriate that he move on.
"In light of all the charges and revelations from the investigations of abuse," it is time "to have someone in there who can lead the church in a new direction," said Nicholas Bisaccia of Philadelphia after attending 11 a.m. Mass at the Cathedral Basilica of SS. Peter and Paul.
District Attorney Seth Williams, whose offices is prosecuting priests who allegedly abused children or protected cleric who did, praised Rigali today and urged Chaput to continue reforms instituted under the cardinal.
"He came into a very difficult situation and I think he tried to do what he thought was best for the Church," Williams, a Catholic, said of Rigali.
"I'm not going to comment on the findings of the Grand Jurors, but I will say that Cardinal Rigali's response to their report has been constructive. Rather than attacking the messengers, he has listened to their criticisms."
Rev. Thomas Reese, former editor of the Jesuit magazine America and author of numerous books on the Catholic hierarchy, said, "I think that with Chaput you will see a much more politically active archbishop than we saw with Cardinal Rigali."
Reese described Chaput as an "in-your-face" leader who is "going to be a real pain in the neck for the Democratic Party."
Columnist and papal biographer George Weigel called Chaput a "great pastor" and predicted he would be a "real jolt of evangelical energy for the archdiocese."
While the sex abuse scandal here might have little to do with the timing of Rigali's departure, it may have factored into Chaput's appointment.
He is credited with responding quickly when Denver priests were accused of sexually abusing minors, according to Matthew Schmalz, an associate professor of religious studies at Holy Cross College in Massachusetts who studies the sexual abuse crisis in this country. Chaput "took a hard, traditionalist stand," he said.
Chaput also helped lead the Vatican's 2009 aggressive investigation into allegations of sexual misconduct by the founder of the conservative religious order Legionaries of Christ, whom the Vatican harshly rebuked.
Nevertheless, Chaput angered victims of clergy sexual abuse by publicly combating their efforts in the Colorado legislature to temporarily lift the civil statute of limitations on sexual assaults so that adult abuse victims could sue their assailants.
Addressing that today, the archbishop said, "The Catholic Church wants to be treated like citizens with equal access to protection of the law - that's all we were asking for in Colorado."
He also denounced some news coverage of the sex abuse crisis as "anti-Catholic" and, according to Schmalz, warned that the church's "zero tolerance" policy - requiring the immediate removal of credibly accused clergy - can "sweep up innocent priests."
But he has been even more forceful in articulating what it means to live as a Catholic. He has regularly rebuked the Obama administration and the Democratic Party.
A month after President Obama's inauguration, Chaput decried what he called a "spirit of adulation bordering on servility" toward Obama by "some . . . Democratic-friendly Catholic writers, scholars, editors and activists. He said, "There's no way to reinvent his record on abortion and related issues with rosy marketing about unity, hope, and change."
In books, homilies and speeches, he regularly exhorts Catholics to turn from secular, materialist values and hew themselves to the church. "His general view is that the Catholic Church has to make a strong countercultural witness - that American society is not now especially congenial to Catholic values," said Schmalz.
Last year, a Boulder, Colo., Catholic elementary school refused to reenroll two children of a lesbian couple because their manner of living was in "open discord" with Catholic teaching. That decision was met with support by traditional Catholics, and criticism from other members of the faith who thought it cruel.
After a barrage of mostly negative media coverage, Chaput used his weekly column in the Denver Catholic Register to make his views known.
"If parents don't respect the beliefs of the church, or live in a manner that openly rejects those beliefs," he wrote, "then partnering with those parents becomes very difficult, if not impossible.
"In many ways times have changed, but the mission of Catholic schools has not," he continued. "The main purpose of Catholic schools is religious; in other words, to form students in Catholic faith, Catholic morality, and Catholic social values."
The Rev. Paul Kuppe, a fellow Capuchin friar and pastor of Our Lady of the Blessed Sacrament Parish at 63d and Callowhill Streets in West Philadelphia, described his old friend as "always a leader."
Kuppe and Chaput attended St. Fidelis College Seminary in Herman, in western Pennsylvania, graduating together in 1967.
"I don't want to label him in any way," Kuppe said Monday. "But if you read his books you see the leaning he has . . . On political issues and perhaps some moral issues, he is very strongly Catholic."
In Chaput's book Render Unto Caesar: Serving the Nation by Living Our Catholic Beliefs in Political Life, he says the separation of church and state does not mean deeply held beliefs must be left outside the voting booth.
"I don't think he has ever forbidden a politician from receiving Communion," Kuppe said. "But he has certainly made his opinion known."
In 2004, the New York Times reported that Chaput had said that anyone who intended to vote for Democratic presidential nominee John Kerry, a pro-choice Catholic, was "cooperating in evil" and needed "to go to confession."
Responding in the Denver Post, Chaput said the Times had misrepresented him. The Denver Archdiocese said Chaput's remarks were "heavily truncated" and "framed" in such a way that he was misconstrued.
Last month, when the U.S. Supreme Court used the First Amendment to strike down a California law that banned the sale or rental of violent video games to minors, Chaput weighed in with a commentary that sided with the dissent by Justice Clarence Thomas.
"When we too readily stretch an individual's right to free speech to include a corporation's right to sell violence to minors, we collude in poisoning our own future," Chaput wrote in an essay picked up by Catholic news agencies.
The Philadelphia-based blogger Rocco Palmo, who writes regularly about the Catholic hierarchy, predicted that while Chaput is a church conservative like the soft-spoken Rigali, his appointment could prove "the most revolutionary shift of leadership this diocese has ever known."
Unlike the "conservative, Irish, institutional Catholicism" that has characterized dioceses in the Northeast, Chaput represents the "vibrant, evangelical post-Vatican II Catholicism of the American West," according Palmo, who writes the "Whispers in the Loggia" blog.
Chaput is no fan of the formal and clerical culture of the Philadelphia archdiocese, according to Palmo. "When he wants to talk to someone, there are no middle layers," he said. "He picks up the phone and calls. He drives. He goes to movies and theater and restaurants, often without other clerics. He has friends, and a life, in the place where he is."
Most observers predict that Chaput will likely be made a cardinal in a few years, as have all Philadelphia's archbishops since Dennis Dougherty got the red cap in 1921.
Although Philadelphia's official Catholic population has remained virtually unchanged at 1.5 million for at least 20 years, Sunday Mass attendance stands at less than 30 percent. Rigali and his predecessor, Cardinal Anthony J. Bevilacqua, closed dozens of parishes and schools because of diminished enrollment.
Since a cardinal is appointed for life, Rigali may continue to serve on Vatican congregations and as a papal elector until he turns 80.
Contact staff writer David O'Reilly at 215-854-5723 or email@example.com.
Inquirer staff writer Paul Jones and Ann Rodgers of the Pittsburgh Post-Gazette contributed to this article.