"We're excited and terrified and feel so very lucky," the couple said in a prepared statement.
The Savages have been working with a surrogate, Jennifer, to conceive since the birth of Logan in 2009. The little boy, now 19 months old, is the biological son of Shannon and Paul Morell.
Both couples have written books about their harrowing experience after an unnamed fertility clinic confused their records and implanted the Morells' embryo in Carolyn Savage's uterus. She carried the fetus for nine months, then handed the child over to his biological parents.
"When we brought Logan into this world, we came to understand his life was a gift," the Savages wrote. "We are humbled again as one very special woman is giving this same gift of family to us. Jennifer, our carrier -- our partner and guardian angel -- has become part of our family. We are in awe of her generosity and our gratitude is beyond measure."
The Savages had tried for another child through surrogacy last year, but Jennifer miscarried. She is now 19 weeks pregnant with twins. The Savages said they did not know the sex of the babies.
"We've been so humbled by every good wish and blessings we've received from real friends like you," they wrote. "When shock and heartbreak came, you comforted. When we started to lose hope about expanding our family, you squeezed our hands in support and told us to not lose faith."
The couple tells their heartbreaking story in their 2011 book, "Inconceivable."
Just four days after finding out she was pregnant, Carolyn Savage went from the high of expecting the child she had tried so hard to conceive, to the unfathomable low of knowing the baby was not hers to keep.
Carolyn Savage had had a history of miscarriages, and she and Sean turned to in vitro fertilization. They already had three other children and hoped for a fourth.
But On Feb. 16, 2009, the Sylvania, Ohio, couple learned that the frozen embryo of another couple had been mistakenly transferred into Carolyn's womb.
The Savages could have fought for custody, or Carolyn could have had an abortion. Tethered to a strong Catholic faith, Carolyn chose to carry the baby she and Sean called "Little Man" to term.
On Sept. 24, 2009, the Savages returned their newborn son, whom they'd held for 30 minutes, to his biological parents -- Shannon and Paul Morell of Sterling Heights, Mich., who named him Logan.
In the months since Logan's birth, the Savages have had a long, painful, somewhat "ambiguous" journey.
"We have three children. Or do we have four? A strange question, but the kind that parents who have lost a child ask themselves from time to time. That absent child is always with you, a loss you feel some days as yearning and other days in a gasp of pain.
"This was a child whom I nurtured and we both protected from the forces conspiring against his survival," writes Carolyn, now 41, in the book's prologue. "Yet I understand that I may never hold him in my arms again and that the next time I see him, he will think of me as a stranger."
Throughout the 36 weeks that Carolyn carried "Little Man," the two couples maintained a respectful relationship. The Morells described in their 2010 book, "Misconception," their own harrowing wait, knowing that with Carolyn's past history of miscarriages, their child might never be born.
In an interview with ABCNews.com, the Savages said that even though they considered it a "gift" to return Logan to his biological parents, the medical mistake tore their lives apart.
Their marriage was under tremendous strain, and after the delivery, Carolyn was diagnosed with post-traumatic stress disorder. Both have sought counseling.
They were in an unusual position: Their son had not died, but he was gone.
"It's a loss that has no closure," said Pauline Boss, professor emeritus at the University of Minnesota, who described the ambiguity in her book, "Ambiguous Loss."
"People have a difficult time resolving this," she told ABCNews.com. "There are no rituals or sympathy cards for them."
"He'll always be my baby, even though he's their son," said Carolyn. "There was no way of entering into a pregnancy and taking a 12-cell embryo and turning it into a human being and not feel a maternal connection to him."
Embryo Mix-Up – What Happened
The embryo mix-up happened at a fertility clinic that a legal settlement prohibits the Savages from naming, but the May 2010 agreement required them to explain in writing what went wrong.
A lab employee where the frozen embryos were stored had labeled Carolyn's birth year as 3/19/1967, rather than 3/19/1969 -- a detail that helped identify the eventual error.
Embryos are stored alphabetically, and when the clinic opened the "S" file, it mistakenly pulled an information sheet for Shannon Savage -- now Shannon Savage Morell, who used her birth name at the time of the original IVF procedure.
From that point on, the Morells' embryos were labeled and associated with the Savage's paperwork, and their sheet was tucked in the back of the file.
Oddly, on the day of the transfer, Carolyn had noticed the wrong birth date when the nurse attached her wrist bracelet.
"It had my name, Sean's name, my Social Security and Sean's and my date of birth," she said. "I said, 'Wait a minute, that's not my birthday,' and made a joke. 'I'm not 40 yet.'"
The nurse took a ballpoint pen and changed the 7 to a 9.
Nine days later, a data-entry person filing the paperwork wondered about the conflicting birth year and rifled through the file, finding the Morells' embryo information sheet in the back.
Until then -- five days after the implantation of the embryo -- no one, not even a doctor, had cross-checked the labels and information sheets.
In the first few weeks after learning of the mistakenly implanted embryo, the Savages didn't tell anyone except their lawyer, their priest and a counselor.
"We made the choices quickly," said Sean. "We also knew that we were embarking on a very different journey, but we didn't stop going in that direction, because we thought it was right. But we didn't have a full understanding of what the pitfalls were."
Their story came not long after the shutdown of an in vitro fertilization center at Ochsner Hospital in Elmwood, La., triggered by a possible mix-up in the labeling of frozen embryos. Similar mistakes have been made in clinics in New York and Great Britain.
Six weeks into the pregnancy, Carolyn developed a clot in her uterus that could have threatened the fetus. The Savages provided the Morells with weekly updates.
"We kept assuring them we wouldn't terminate and would never fight for custody," said Carolyn. "But Sean and I were emotionally tapped."
So far, they have had two visits with Logan, who is now 19 months old. The Savages have no formal agreement with the Morells about future visits, or whether Logan will ever know the truth about his birth. "His mom and dad will decide what's best for him," said Sean.
Safety Protocols for IVF
The Savages say they have had to start their lives up again with their three children -- Drew, now 16; Ryan, 13; and Mary Kate, 2. Though they've received support from their church and friends, sometimes the simplest things throw the Savages off guard.
"It was the like the elephant in the living room," said Carolyn. "People were so terrified of saying the wrong thing. Anytime there is a challenging situation or a loss, people don't know what to say. I still feel that now."
As part of the settlement, the clinic agreed to provide assurances in writing that new protocols would be established.
In their book, the Savages encourage those seeking IVF to have pointed conversations with doctors regarding how their embryos are handled.
"We were lucky to come out the other side of this," said Carolyn. "Make no mistake. What happened, the mistake at the clinic, the pregnancy and loss of Logan, we will have to live with this for the rest of our lives. As time goes on, we'll be better at weaving it into the fabric of our lives."
"It was an unacceptable, cruel situation to be put in," said Sean. "I don't want anyone to think it was an easy road to walk. But, still, we got through it and our decision was fundamentally good."