Under the programme, the embryos come from healthy patients who are younger than 35 years and received successfully in vitro fertilisation (IVF) treatment and decided to have no more children.
The embryo adoption programme was established by the Institut Marques to give couples the opportunity to either donate or adopt unused frozen embryos.
Under Spanish legislation, fertility clinics are permitted to donate frozen embryos to other patients once the other couple has disengaged from them.
The pioneering programme registered 550 births up to the end of April this year.
New figures show that a total of 27 Irish couples and 103 British couples have taken part in either embryo donations or embryo adoptions.
The programme was established in 2004.
The figures show a high success rate of 81pc in the 27 Irish couples participating, resulting in 22 births.
By comparison, 103 British patients did an embryo donation or adoption, which resulted in the birth of 62 babies, equating to a success rate of around 60pc.
Irish couples comprise just under 4pc of the total number of births to mothers from 28 countries, according to The Medical Independent.
On its website, the clinic explains the differences between embryo adoption and donation.
It said that: "The difference lies within the legal situation. For the donation programme the embryos come from couples who explicitly and in writing cede their embryos to other couples.
In the adoption programme, the destination of the embryos has not been chosen and, therefore, they are legally under the protection of the centre."
It said that in any of these two cases it is only necessary to sign the consent form for the assisted reproduction technique.
The clinic pointed out that "due to the restrictive laws in other states, patients come from different countries".