Lord Justice General Lord Hamilton delivers the court's decision
Judges have accepted an application by the Lockerbie bomber to drop his second appeal against conviction.
The permission of the High Court in Edinburgh was required before the proceedings by Abdelbaset Ali al-Megrahi could be formally abandoned.
It comes as the Scottish Government considers his requests for either release or transfer to a Libyan jail.
Seven US senators have urged Justice Secretary Kenny MacAskill to make Megrahi serve his sentence in Scotland.
The Libyan's legal team outlined his current state of health to the appeal hearing.
QC Margaret Scott said: "The court is aware of Mr Megrahi's medical condition in that he has progressive prostate cancer.
"This has now reached the terminal stage and my client's condition has recently worsened very considerably.
Megrahi's legal team applied last week to drop his second appeal
"Up-to-date medical reports from three eminent experts also concurred in the view that he has a very aggressive cancer, that his condition is grave and that the prognosis is extremely limited."
By dropping his appeal, Megrahi has removed one potential obstacle to his transfer to a jail in his homeland.
However, a Crown appeal against the length of his sentence is still ongoing.
Scotland's senior law officer, Lord Advocate Elish Angiolini QC, will now have to consider whether that should also be dropped.
A Crown Office statement said its appeal was "entirely separate" from Megrahi's appeal.
It said the lord advocate had not received any request to indicate whether the appeal would continue.
"The lord advocate has always been prepared to give any request her full and prompt consideration," it stressed.
It added that no information had been received about Megrahi's current medical situation which might need to be taken into account in handling the appeal.
Scotland's senior judge, the Lord Justice General, Lord Hamilton, said it was important the Crown appeal issue was resolved quickly.
"It appears to the court to be of the utmost importance that an early decision be made by the lord advocate as to whether she is to insist or not to insist on that appeal," he said.
He added: "The court urges her to reach a decision on that matter without undue delay."
Some relatives of the victims said the dropping of the appeal meant that many questions would now go unanswered.
The Reverend John Mosey, who lost his daughter in the bombing, described it as a "very sad day for Scottish justice".
"My feeling is that I would be happier if he was going home after the hearing of his appeal, either as an innocent man or as a guilty man," he said.
"Either way, my personal feeling is 85% that he is an innocent man - of this crime anyway - having sat through the whole of the trial in Holland."
It emerged last week that the Libyan had applied to withdraw his second appeal against conviction.
It prompted claims he had been put under pressure to make the move - a suggestion the Scottish Government has strenuously denied.
Rev John Mosey, father of one of the victims, gives his reaction
The Justice Secretary is currently considering whether or not to release Megrahi on compassionate grounds or to allow his transfer to a prison in Libya.
He is expected to announce his decision within the next two weeks.
A letter from seven US senators has urged Mr MacAskill not to release Megrahi from jail.
The 57-year-old is currently serving a life sentence with a minimum of 27 years after being convicted in 2001 of the 1988 bombing which killed 270 people.
The senators want him to serve out the rest of his sentence in Scotland.
The Scottish Government has also come under pressure to recall parliament to discuss the issue.
However, presiding officer Alex Fergusson said that after weighing up "all the factors very carefully" he had decided against such a move.
LOCATIONS WHICH SHAPED MEGRAHI'S TRIAL
1. Tripoli, capital of Libya. Megrahi was born here on 1 April 1952, and worked - according to the FBI - for Libyan intelligence services.
2. Malta. Megrahi's day job, as security chief for Libyan Arab Airlines, took him to their office on the island. From there he would travel to Zurich. The bomb began its journey here in December 1988.
3. Zurich, Switzerland. The bomb's timing device was made and purchased here.
4. Frankfurt, Germany. On arrival, a suitcase later found to have contained the bomb was transferred from an Air Malta jet to a flight bound for London Heathrow.
5. London's Heathrow Airport. Pan Am flight PA 103 took off from Heathrow at 1825 GMT on Wednesday, 21 December 1988.
6. Lockerbie, Scotland. The bomb on Flight PA 103 exploded above the Scottish village at 1902 GMT.
7. Camp Zeist, Netherlands. Here, in a landmark trial, Scottish judges convicted Megrahi in 2001.
8. HMP Barlinnie. Megrahi served the first part of his sentence in this Scottish prison.
9. HMP Greenock. Megrahi was transferred from Barlinnie to Greenock in 2005.
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