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.
