Doctors said the girls, identified only as Jodie and Mary, will die within months if they remain together, but that Jodie could survive on her own. The ruling by the three judges of the Court of Appeal was unanimous.
The case may not be over, however - the parents were permitted to appeal to the House of Lords, Britain's highest court. They were uncertain whether they would do so.
The twins, joined at the lower abdomen, were born Aug. 8 at St. Mary's Hospital in Manchester.
``Though Mary has a right to life, she has little right to be alive. She is alive because and only because - to put it bluntly but nonetheless accurately - she sucks the lifeblood of Jodie and her parasitic living will soon be the cause of Jodie ceasing to live,'' Justice Alan Ward said, summarizing the judgment.
``Jodie is entitled to protest that Mary is killing her. Nobody but the doctors can help Jodie. Mary sadly is beyond any help.
The court had struggled with the issue of whether the surgery would amount to intentionally killing Mary.
``Mary's death would not be the purpose of the operation, although it would be its inevitable consequence. The operation would give her, even in death, bodily integrity as a human being. She would die, not because she was intentionally killed, but because her own body cannot sustain her life,'' Justice Robert Walker said.
Two medical specialists appointed by the court to review the case endorsed surgery.
The parents, identified only as Roman Catholics from the Mediterranean island of Gozo, Malta, had appealed against a lower court ruling in favor of surgery. They were supported by the Roman Catholic archbishop of Westminster, Cormac Murphy O'Connor. The justices on Friday lifted an order barring the identification of the island.
During hearings earlier this month, Tim Owen, a barrister appointed to represent Jodie's interest, argued that Mary had no chance of long-term survival, and it was ``unreal'' to consider Mary's interests separately from those of Jodie.
``Without Jodie, Mary will die. With Mary, Jodie will die,'' Owen said.
``The purpose of the operation is wholly to maintain life and not to accelerate death by mercy killing or otherwise,'' Owen said.
David Harris, a lawyer appointed to represent Mary, argued that she had an interest in continuing her life unless proven otherwise.
``Although this is a life of short duration very severely handicapped, there is insufficient evidence that it is so intolerable as to render it in the child's best interests that it should end,'' Harris said.
The parents, in a statement read in court Sept. 4, said they had come to England ``to give our babies the very best chance for life in the very best place.'' By doing so, they placed the decision on the twins' fate under British jurisdiction.
``Now things have gone very badly wrong and we find ourselves in this very difficult situation...We believe that nature should take its course. If it's God's will that both our children should not survive then so be it,'' they said.