The babies were born on August 3rd at an undisclosed location and their birth has already been recorded on the civil register, La Stampa reported.
Their birth came as their genetic parents launched a custody battle, with the first court hearing due to take place in Rome on Friday.
In a case that exposed serious flaws in the Italian medical system, the embryos of another couple were mistakenly implanted in an Italian woman following an IVF blunder at a hospital in Rome last December.
The genetic parents, who have not been named, were identified through DNA tests in April.
The babies were born by caesarean section.
"We need peace...we have already suffered a lot in recent months, for us it's finally time to be a family,” the birth parents, named as Paolo and Francesca, were quoted in La Stampa as saying.
The mix-up, which was possibly due to the similarity in surnames of the two couples, happened on December 4th, when four different couples were receiving treatment at a specialist fertility unit at the Sandro Pertini hospital.
Four women underwent fertility treatment at the hospital that day to have viable embryos implanted, three of whom became pregnant as a result of the procedure. The biological parent's own IVF pregnancy ended in a miscarriage.
Although Italian law stipulates that whoever gives birth to the child is the mother, the biological parents pledged last month to fight the case “at all the legal levels”.
“We recognize their suffering and this makes us feel bad, but we have been available to meet them," they told La Stampa.
"Instead, our request to meet was not even answered."
Michele Ambrosini, the lawyer representing the birth mother, told The Local last month that the case would be “very difficult and distressing for both couples”.
“It’s difficult to say what the outcome of this will be, as there hasn’t been a precedent case,”he said.
"Either way, it will be very difficult and distressing for both couples."