Bishop Eaton won, 600-287, on the fifth ballot.
She seemed as shocked as everyone else at her election, joking: "I just wanted there to be a conversation [about a new bishop]. I just didn't think it would get this far out of hand."
She will take office Nov. 1. Nominees don't campaign, but voting members of the Churchwide Assembly can initially write the name of any ordained minister on a piece of paper, and the winner is gradually winnowed from the seven top finishers.
The denomination has lost 500,000 members and 647 of 10,000 congregations to schism since it gave permission four years ago to ordain and install partnered gay pastors.
Bishop Eaton, 58, is considered a centrist, while other finalists were viewed as more theologically liberal.
During a brief address before the third ballot, she was the only one of four remaining nominees to directly address concerns of theological conservatives who had remained in the denomination.
She said she supported the decision to allow partnered gay clergy but that being an inclusive church meant respecting those with a different understanding of scripture and doctrine.
"Those people also have a voice in this church. We need to make room for those who do not agree with us but agree with our claim upon the cross," she said.
She stressed the importance of maintaining Lutheran theological distinctives while reaching beyond a Nordic ethnic base. She also spoke of having a spiritual director to deepen her life of prayer and discernment of God's guidance.
After her initial remarks, she shot from a distant third to a strong lead in the balloting.
Bishop Judith Crist of Montana, who chairs the Council of Bishops, won just 84 of 907 votes on the fourth and penultimate ballot, which eliminated her.
At a news conference, Bishop Eaton elaborated on the need to recognize and heal divisions.
Lutheran theology is filled with paradox, she said, so that it would be a truly Lutheran witness for people to agree to disagree after "maybe being a little bit molded by an unfortunately very fractious and divided civil discourse."
Asked about nascent discussions with new denominations that broke with the ELCA after 2009, she said it would take work on both sides "to come to a place where we can have an open and civil dialogue."
"The manner in which those denominations were formed has been extremely painful to our church. It will not be something that will be quickly forgotten," she said. "But we are supposed to love our enemies ... and since these are actually our brothers and sisters -- and families might be tougher than enemies -- we will do what we can through God's grace because that is the only way that is going to happen."
The Episcopal Church also has a female presiding bishop -- Bishop Katharine Jefferts Schori, elected in 2006 -- but that denomination is half the size of the ELCA.
The second-largest Lutheran body in the United States, the Lutheran Church-Missouri Synod, doesn't ordain women.
The first female bishop in the ELCA -- and the second in the world -- was Bishop April Larson, elected in 1992.
Bishop Eaton thanked Bishop Larson for blazing the trail. When she was ordained in 1981, she said, she was usually the only woman at clergy gatherings where someone would say she wasn't "strident like other women."
Her reply was, "I don't have to be because they were the pioneers who made it possible for me."
Bishop Hanson pledged to pray for her and work for a smooth transition, calling her "a wise theologian with experience beyond belief in a church that lives with its decisions."
Bishop Donald McCoid, the former Pittsburgh bishop who is now the denomination's top ecumenical officer, praised Bishop Hanson's leadership while saying that the Holy Spirit and the church had spoken.
"The prayers of the church will surround her," he said. "She has been dedicated to ecumenism as well as Lutheran identity."
Bishop Eaton's husband, the Rev. Conrad Selnick, is an Episcopal priest. They have two grown daughters.
The Rev. Donald Green, an ELCA pastor who serves as executive director of Christian Associates of Southwestern Pennsylvania, said he believed her election was good for theologically traditional Lutherans within the denomination.
"Today the Spirit was here and God is making things new in a very new way for us," he said.
Pastor Heather Lubold of Berkeley Hills Lutheran Church in Ross said Bishop Eaton "was able to acknowledge the challenges facing the church while affirming who we are as a church committed to being present in our diverse world with the faith and love of the Gospel of Jesus Christ."
A native of Cleveland, Bishop Eaton earned a bachelor's degree in music education from the College of Wooster before attending Harvard Divinity School.
She has been bishop of the Synod of Northeastern Ohio since 2006, and had served as pastor of Messiah Lutheran Church in Ashtabula, Ohio, for 15 years before that.