Several judges stressed the need for legislation in this area, noting that there are no such dedicated laws.
The parents of the twins and the twins' surrogate, the genetic mother's sister, comforted each other as the ruling was handed down.
Earlier this year the State sought to overturn a May 2013 High Court order of Mr Justice Henry Abbott in which he defined maternity as based on genetic or blood links and ruled the genetic parents were entitled to be registered as the legal parents of the twins.
The State's position is that a woman who gives birth to a child is the mother of the child and that motherhood as a matter of fact and common sense involves pregnancy and cannot be based on genetics.
The State also contended the position of the genetic parents and twins would be addressed in forthcoming legislation and that it is open to the genetic parents to adopt the twins.
The twins were born to a sister of the genetic mother who, due to a disability, was unable to carry a pregnancy herself.
The arrangement between the surrogate and genetic parents was described as a gesture of love by the surrogate.
The genetic parents took the case after the Registrar of Births refused to register the genetic mother as the legal mother of the twins on their birth certificates.
The surrogate was registered as the twins mother while the genetic father was registered as their legal father.