Apple (NSDQ: AAPL) continues to stay silent on the issue of CEO Steve Jobs’ health, but the Methodist University Hospital Transplant Institute confirmed late Tuesday that Jobs underwent a liver transplant at its facility in Memphis, Tennessee, and that the pancreatic cancer survivor has an “excellent prognosis” Bloomberg reports.

The hospital posted a statement by Dr. James D. Eason, program director and chief of transplantation, on its web site, after Jobs gave the hospital permission to make the disclosure. The statement also said that Jobs underwent a complete transplant evaluation and was approved with standard policies. Eason: “He received a liver transplant because he was the patient with the highest MELD score (Model for End-Stage Liver Disease) of his blood type and, therefore, the sickest patient on the waiting list at the time a donor organ became available. Mr. Jobs is now recovering well and has an excellent prognosis.”

Jobs went on medical leave six months ago, and was expected back at work at the end of the month. However, he was spotted on campus this week, and was quoted in a press release on Monday about selling more than 1 million of the latest iPhones over the weekend. Steve Dowling, an Apple spokesman, told Bloomberg: “Steve continues to look forward to returning to Apple at the end of June.”

The company’s secrecy has draw tremendous criticism, and was the subject of an article in the NYTimes today, which wrote that the company’s no-comment approach was “unparalleled.”