Glasspool and another female bishop are also the first two women bishops ordained in the 114-year history of the Diocese of Los Angeles.
Glasspool and the Rev. Canon Diane Jardine Bruce were elected last December.
The Episcopal Church, which is the Anglican body in the United States, caused turmoil in the church in 2003 by consecrating the first openly gay bishop, V. Gene Robinson of New Hampshire.
Breakaway Episcopal conservatives have formed a rival church, the Anglican Church in North America.