Al-Megrahi was found guilty in 2001 of the bombing of a Pan Am flight over the Scottish town of Lockerbie that killed 270 people.
The former Libyan intelligence agent is serving a life sentence in Scotland.
Al-Megrahi, who was tried in the Netherlands, was convicted while his Libyan co-defendant was acquitted.
"My view is that no reasonable tribunal, applying the rules of evidence, law and procedure, could and should have convicted him"
Robert Black, law professor at the University of Edinburgh
The three Scottish judges, acknowledged the difficulty of the evidence, when they issued their verdict.
"We are aware that in relation to certain aspects of the case there are a number of uncertainties and qualifications," they said.
"However,... we are satisfied that the evidence... does fit together to form a real and convincing pattern."
The judges decided that the evidence showed the bomb was placed aboard a plane in Malta.
It was then transferred onto a Pan Am 'feeder' flight at Frankfurt before ending up on Flight 103 from London Heathrow to New York on December 21, 1988.
Critics have questioned the reliability of the witness who identified Megrahi, the forensic evidence and whether the bomb was really loaded in Malta or at Heathrow.
"My view is that no reasonable tribunal, applying the rules of evidence, law and procedure, could and should have convicted him," Robert Black, a law professor at the University of Edinburgh, said.
Libya has paid more than $2 billion in compensation to victims' relatives since telling the United Nations in 2003 it "accepts responsibility for the actions of its officials".
The North African country is seeking international rehabilitation after Washington had branded it for years a rogue state,
But lawyers and analysts say that carefully worded formula could enable Libya to deny any role if Megrahi's conviction were appealed.
Some believe it may even demand compensation from the United States and Britain.