While some Episcopal churches had blessed same-sex unions, this move makes the full marriage rite available to same-sex couples throughout the denomination.
The news comes in the wake of controversy over the initial postponement of the baptism.
The couple had used social media to go public with the controversy over their son's baptism in an Episcopal church.
The Episcopal priest risked his career when he came out in the 1970s.
The Archbishop of Canterbury, spiritual head of the worldwide Anglican Communion, pleas for respect for LGBT people ahead of his African visit.