An Ohio woman who was implanted with the wrong embryo has given birth to a "healthy baby boy" and given him up to his biological parents, her family said in a statement.

Carolyn Savage, 40, and her husband Sean offered their "heartfelt congratulations" to Paul and Shannon Morell -- the boy's biological parents, according to the statement released late Friday.

The child was delivered at St. Vincent Mercy Medical Center in Toledo, Ohio on Thursday.

"We wish Paul, Shannon, their twin girls and their new baby boy the best, as they move forward with their lives together," the Savage family statement said.

They also asked for privacy, saying "our family is going through a very difficult time and requests privacy in the days ahead."

Savage learned of the mistaken medical procedure about two months into her pregnancy, but decided to give birth to the child anyway and hand over the baby to the Morells after delivery.

Such mistakes are rare but have often ended with the birth mother going through an abortion or putting the child up for adoption.

Savage decided to go ahead with the pregnancy due to her Catholic religious beliefs.

She went public with her decision in the final weeks of her pregnancy, telling NBC television the decision would be a difficult one.

"Of course, we will wonder about this child every day for the rest of our life," she said.

"The hardest part is going to be the delivery," she said at the time. "I remember communicating with the mother of this child as to what I was envisioning and hoping for. I said, 'We want a moment to say hello, and goodbye.'"

Her husband, Sean, told the Toledo Free Press "We didn't have to discuss it. We came to an instantaneous conclusion; this was the path that we had to go down."

The couple already has three children. They resorted to in vitro fertilization after reproductive problems and a series of miscarriages.

"Our family is deeply grateful for the support and prayers of so many people from around the world," the statement said.

The two couples initially contacted each other anonymously through lawyers but eventually met face-to-face in what Savage has said was a cordial relationship.

Attorneys are working out the legal details, with the Savages' lawyers saying they want the fertility clinic that conducted the procedure to accept responsibility for the mistake.