"The commission is of the view, based upon our lengthy investigations, new evidence we have found and other evidence which was not before the trial court, that the applicant may have suffered a miscarriage of justice," the panel said in a statement summarising its 800-page report.
Al-Megrahi, who was tried in the Netherlands, was convicted while his Libyan co-defendant was acquitted.
The three Scottish judges, acknowledged the difficulty of the evidence, when they issued their verdict.
"If Mr Megrahi is innocent he should be allowed to return home to his family"
John Mosey, father of a Lockerbie victim
"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 an aircraft 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 al-Megrahi, the forensic evidence and whether the bomb was really loaded in Malta or at Heathrow. Families of the victims remain divided on al-Megrahi's conviction. Some say the evidence against him is at best circumstantial.
John Mosey, whose 19-year-old daughter Helga died in the Lockerbie attack, said on Thursday: "If Mr Megrahi is innocent he should be allowed to return home to his family."
A statement from the British families of victims said: "The group has been concerned that the full and true facts about the bombing have never been fully explained. Now we ask that this appeal leads to more information emerging about the bombing."
Al-Megrahi has always maintained his innocence. His lawyers - and families of some Lockerbie victims - also have long argued that his 2001 conviction was unsound.
Libya has welcomed the court decision to allow al-Megrahi the right to appeal.
"The decision opens the door of hope regarding the innocence of Abdel Basset al-Meghrahi ... This decision will have good consequences," Mohammed Elzwi, a Libyan official dealing with the Lockerbie issue and former ambassador to Britain, said in a statement.
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 has been seeking international rehabilitation after Washington had branded it for years a rogue state but lawyers and analysts say that the carefully worded formula could enable Libya to deny any role if al-Megrahi's conviction is overturned.
Some believe it may even demand compensation from the United States and Britain.