Sarah Murnaghan’s family said they were “thrilled” the six-hour surgery to implant adult lungs went smoothly and that she had done “extremely well”.
The family had challenged a US policy relegating under-12s to the bottom of the adult organ donation list.
Analysts have warned the judge’s decision set a dangerous precedent.
The Obama administration declined to intervene in Sarah’s case, arguing transplant policy should be made by doctors and scientists rather than the government.
Children under 12 have priority for paediatric lung donations, but far fewer paediatric lungs are donated than adult lungs.