Eva Brunne, 55, was installed as bishop of Stockholm in a ceremony at Uppsala Cathedral.
She was elected in May, beating a colleague 413-365 in a vote cast by an equal number of clergy and lay people.
Brunne is in a registered partnership with the Rev. Gunilla Lindén and they have a 3-year-old son.
Sweden also allows gay couples to marry and, in October, the Church of Sweden general synod voted 176-62 to begin marrying same-sex couples.
About 74 percent of Swedes are members of the church although only 2 percent of them are regular churchgoers.