Catechism of the Catholic Church §2296 — excerpt
Organ transplants are in conformity with the moral law if the physical and psychological dangers and risks incurred by the donor are proportionate to the good sought for the recipient.
This translation is under copyright, so only the cited words are quoted here. Follow the link for the full text. Translation: English translation of the Catechism of the Catholic Church, 2nd ed. (Libreria Editrice Vaticana), as posted at vatican.va.