In a statement, Archbishop Nienstedt said he submitted his resignation to Pope Francis "to give the archdiocese a new beginning amidst the many challenges we face."
"The Catholic Church is not our church, but Christ's church, and we are merely stewards for a time," he said. "My leadership has unfortunately drawn away from the good works of his church and those who perform them. Thus, my decision to step down."
On June 5 the Ramsey County Attorney's Office filed criminal and civil charges against the archdiocese alleging it failed to protect three boys who were sexually abused in 2008-2010 by Curtis Wehmeyer, a former priest of the archdiocese.
Wehmeyer was convicted of the abuse and is serving a five-year prison sentence. He was dismissed from the priesthood in March.
Archbishop Nienstedt, 68, was appointed coadjutor archbishop of St. Paul and Minneapolis in 2007, and installed as its archbishop in June 2008, succeeding Archbishop Harry J. Flynn, who retired.
Prior to taking the helm of the archdiocese, Archbishop Nienstedt was bishop of New Ulm, Minnesota, from 2001 to 2007, and auxiliary bishop of Detroit from 1996 to 2001.
"It has been my privilege the last seven years to serve this local church," Archbishop Nienstedt said in a statement. "I have come to appreciate deeply the vitality of the 187 parishes that make up the Archdiocese of St. Paul and Minneapolis. I am grateful for the support I have received from priests, deacons, religious men and women and lay leaders, especially those who have collaborated with me in the oversight of this local church."
He added: "I leave with a clear conscience knowing that my team and I have put in place solid protocols to ensure protection of minors and vulnerable adults."
Archbishop Nienstedt requested prayers for "the well-being of this archdiocese and its future leaders."
"I also ask for your continued prayers for me," he said.
Bishop Piche, 57, was ordained as an auxiliary for St. Paul and Minneapolis in 2009.
"The people of the Archdiocese of St. Paul and Minneapolis needed healing and hope. I was getting in the way of that, so I had to resign," he said in a statement. "It has been a privilege to serve this local church, and I will continue to hold everyone in the archdiocese in my prayers."
Archbishopd Hebda plans to serve both the Minnesota and Newark archdioceses until Pope Francis names Archbishop Nienstedt's successor.
In his statement, he noted that the position of an apostolic administrator is temporary and his role "is not to introduce change, but rather to facilitate the smooth continuation of the ordinary and essential activities of the church, while advancing those positive initiatives to which the archdiocese is already committed."
Still, he said, he hoped to meet as many people as possible in the archdiocese while still fulfilling his responsibilities in Newark.
"As the universal church prepares to embark on a Year of Mercy, I look forward to getting to know this local church and experiencing in a new context the marvelous ways in which the Lord works through his people to make his grace and healing presence known and felt, even in the most challenging of times," Archbishop Hebda said.
The Archdiocese of St. Paul and Minneapolis filed in January for reorganization under Chapter 11 of the U.S. Bankruptcy Code amid mounting claims of clergy sexual abuse. In 2013, the Minnesota Legislature lifted the civil statute of limitations on claims of child sexual abuse for a three-year period.
In May, the archdiocese announced that it would sell archdiocesan offices, including the archbishop's residence, as part of the reorganization.