Please see the following decisions of the Islamic Fiqh Assembly of the Muslim World League (8/1)

All praise be to Allah and peace and blessings be upon the seal of prophets. The council of the Islamic Fiqh Assembly in its eighth session addressed the issue of organ transplantation…. After scrutinizing the proofs cited by each group of scholars, the council of the Assembly concluded that the view of those who approve of the permissibility of organ transplanting is the more acceptable, and therefore, council has decided the following:

 First: It is permissible to remove an organ from one person`s body that is still alive and transplant it into another person`s body that needs this organ to save his life or to restore an organ`s regular function. The permissibility here is conditioned by the following,

1.      Such an act will not cause any harm or weakness to the donor or prevent him from living his life normally, as the Islamic rule states that "Harm can not be warded off by an equivalent or a greater harm." Furthermore, donation in such a situation would be equivalent to throwing oneself into certain destruction, which is impermissible from the Islamic viewpoint.

2.      The donor gives the organ willingly, with no compulsion.

3.      The transplantation of that organ is the only medical treatment for the patient.

4.      That the success of both removing the organ and transplanting it is certain or at least most likely.  

Second: Organ transplantation is permitted in the following situations:

1.      Transplanting an organ from a dead person to a living person whose life depends on receiving that organ, on the condition that the donor was legally accountable and that he gave permission for it before his death.

2.      Taking the organ from an edible slaughtered animal, when necessary, to be transplanted into a human body. 

3.      Using part of a person’s body (e.g. a bone or part of the skin) and transplanting or grafting it onto another part of the same person’s body, in the case where he needs this to be done.

4.      Placing metal or other materials into the human body to treat an illness, such as in the joints and heart valves, and for other diseases. The four cases described above are deemed permissible when the conditions discussed above are attended to.