Kurtz has been vice president of the body since 2010. Cardinal Daniel DiNardo of Galveston-Houston, who also ran for president, was elected vice president at the bishops' meeting in Baltimore.
The leadership change comes at a time when the Catholic Church appears to be on the threshold of big changes. Pope Francis, who succeeded Benedict XVI in March, recently started a survey of lay Catholics on issues such as divorce, contraception, homosexuality and abortion.
Kurtz was elected on the first ballot with 125 votes. DiNardo got 25 votes and Archbishop Charles Chaput of Philadelphia 25, the National Catholic Reporter said.
DiNardo defeated Chaput for the vice presidency in a runoff, 147-87.
Kurtz, 67, was ordained a priest in Allentown in 1972. He became bishop of Knoxville, Tenn., in 1999 and Louisville archbishop in 2007.
DiNardo, 64, was ordained in Pittsburgh in 1977. He was bishop of Sioux City, Iowa, from 1998 to 2004, and then moved to Texas, where he was coadjutor bishop and then archbishop in the Houston-Galveston diocese.
In 2007, DiNardo became the first Texas bishop to be elevated to the College of Cardinals.