The 71-year-old Gregory, previously the archbishop of Atlanta, becomes the first African American to lead the Washington archdiocese.
Gregory replaces Cardinal Donald Wuerl, who resigned in October amid allegations that he covered up multiple abuse scandals while serving as a bishop in Pittsburgh.
Wuerl had replaced Cardinal Theodore McCarrick, who was defrocked by the pope after a Vatican-backed investigation concluded he sexually abused children and adults during his time as a priest in New York and a bishop in New Jersey. It was the first time a cardinal had been dismissed from the priesthood for abuse.
Despite his resignation, Wuerl remains in good standing in the church and served in a caretaker role while the search for his replacement was conducted. On Tuesday, he gave the opening remarks introducing Gregory.
"All of us here recognize his many gifts and welcome him as a faith-filled pastor," Wuerl said. "It is clear that Pope Francis sends us a bishop attuned with the signs of the times and endowed with great pastoral ability."
Gregory, in his remarks, directly addressed the recent scandals.
"We stand at a defining moment for this local faith community," he said. "Our recent sorrows and shame do not define us. Rather they serve to chasten and strengthen us."
Calling his installation "an indescribably humbling moment," Gregory pledged to create an open and inclusive environment.
"I want to be a welcoming shepherd," he said. "We begin a journey together on undeniably choppy seas."
Gregory is credited for his leadership of the U.S. church during a moment of crisis. As president of the U.S. bishops conference, he persuaded church leaders to adopt toughened penalties for abusers in 2002.
In Atlanta, Gregory was embroiled briefly in a scandal of his own in 2014 after the archdiocese used $2.2 million in donations to buy and renovate a swank new home for the archbishop. The mansion was later sold, and Gregory apologized following an outcry from parishioners.
A native of Chicago, Gregory takes over a relatively small archdiocese that has always held outsized importance due to its location in the nation's capital. Washington archbishops are traditionally elevated to cardinals; if that happens, Gregory would become the first African American cardinal.
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