Francis finally accepted his resignation on Friday in a letter in which he praised Wuerl's "nobility" and said the cardinal would stay on until his successor is appointed.
Wuerl said in a statement that he was "deeply touched" by the pope's letter and that his replacement would "allow all of the faithful, clergy, religious and lay, to focus on healing and the future".
He also apologised for "any past errors in judgement".
A sweeping US grand jury report released in August revealed credible allegations against more than 300 predator priests and identified over 1,000 victims of child sex abuse covered up for decades by the Catholic Church in the state of Pennsylvania.
The report is thought to be the most comprehensive to date into abuse in the US church, but while prosecutors have filed charges against two priests, the vast majority of crimes happened too long ago to prosecute under current laws.
Despite facing numerous calls for his resignation, including from his own clergy, Wuerl said at the time the report confirmed he had acted with "diligence, with concern for the victims and to prevent future acts of abuse".
The case triggered a storm in August when Archbishop Carlo Maria Vigano, a former Vatican envoy to Washington, accused the pope of ignoring allegations that McCarrick had abused a teenager decades ago.
On Saturday, Francis ordered an investigation into the Vatican archives over the allegations.
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