Cardinal Timothy Dolan, the archbishop of Milwaukee at the time, also transferred $57 million (£37.5 million) into a trust to protect it from legal claims by sex abuse victims the documents show.
The papers were made public on Monday as part of a deal reached in federal bankruptcy court between the archdiocese and victims suing it for fraud.
Cardinal Dolan - now president of the US Conference of Catholic Bishops and the nation's most prominent Roman Catholic official - has been accused by victims of taking part in a decades-long cover-up by the archdiocese of Milwaukee of sexual abuse perpetrated by priests.
The documents provide new details on Cardinal Dolan's plan to pay some abusers to leave the priesthood and move the $57 million into a trust for "improved protection" as the Milwaukee archdiocese prepared to file for bankruptcy amid dozens of abuse claims. A Vatican office approved the request to move the money.
Victims' attorneys have accused the cardinal of trying to hide the $57 million from victims. In a statement released Monday, the church leader called any such suggestion an "old and discredited" attack.
In his letter to the Vatican, Cardinal Dolan wrote, "By transferring these assets to the Trust, I foresee an improved protection of these funds from any legal claim and liability."
The documents also show that then-archbishop Dolan sought to push problem priests out of the priesthood after people began coming forward with abuse claims in the early 2000s.
He wrote to then-Cardinal Joseph Ratzinger, the future pope, in July 2003 asking to dismiss Daniel Budzynski. Abuse allegations against Mr Budzynski stretched back to the 1970s, and Cardinal Dolan told Cardinal Ratzinger that "as victims organise and become more public, the potential for true scandal is very real."
The Vatican removed Mr Budzynski from the priesthood in 2004.
At least three priests accused of sexual abuse received payments when they left the priesthood before Cardinal Dolan's arrival, according to the documents. Six more left under him, accepting the archdiocese's offer of $10,000 (£6,580) when they voluntarily agreed to leave and another $10,000 when Vatican officials announced their decision about the priest's future.
As of June 30, 2012, the archdiocese had spent nearly $30.5 million (£20.05million) on litigation, therapy and assistance for victims and other costs related to clergy sex abuse, according to its annual statement. It faces sex abuse claims from about 570 people in bankruptcy court, although some involve lay people or priests assigned to religious orders, not the archdiocese.
Similar files made public by other Roman Catholic dioceses and religious orders have detailed how leaders tried to protect the church by shielding priests and not reporting child sex abuse to authorities. The cover-up extended to the top of the Catholic hierarchy.
Correspondence obtained by The Associated Press in 2010 showed then-Cardinal Ratzinger had resisted pleas in the 1980s to defrock a California priest with a record of molesting children. He led the Vatican office responsible for disciplining abusive priests before his election as pope.
Edited by Hannah Strange.