Bishop Michael, from North Carolina, succeeds the Episcopal Church's first female presiding bishop, Katharine Jefferts Schori, and will be installed on 1 November.
The presiding bishop is the leader of the American branch of the Anglican Communion.
The Episcopal General Convention, the Church's top legislative body, voted overwhelmingly in favour of Bishop Curry's appointment on Saturday.
It voted 121 to 53 to appoint Mr Curry, while the House of Deputies - where clergy and laity can vote - voted 800 to 12 in favour of appointing him.
The decision comes at a time when racial tensions in the US are high after the Charleston massacre, arson attacks against several black-majority churches and several incidents of alleged white police brutality against unarmed black suspects in the past year.
Bishop Michael said his appointment as the first African-American leader of Episcopalians was "a sign of our church growing more deeply in the spirit of God and in the movement of God's spirit in our world.
He added: "We've got a society where there are challenges before us. We know that. And there are crises all around us. And the church has challenges before us.
"We are part of the Jesus movement, and nothing can stop the movement of God's love in this world.
"The truth is we are brothers and sisters of each other," Curry said. "The hard work is to figure out how we live as a beloved community, as the human family of God."