The ruling will mean Fhimah, 44, is immediately free to leave the Netherlands and return to Libya.
Al-Megrahi, 48, has 14 days to file an appeal against his conviction, which carries a mandatory life sentence in a Scottish prison.
Both the accused were ushered into the courtroom wearing traditional Libyan dress and looked calm and collected as the judges took their seats.
The verdicts were read out by presiding judge Lord Sutherland, who was asked by the court clerk if the judges had reached a verdict.
Lord Sutherland answered ‘‘guilty’’ when asked for the verdict in the case of Al Megrahi.
The judge added that the verdict was subject amending the charge. The charge was then amended by the clerk to delete a reference relating to the delivery of the suitcase containing the bomb to Malta.
But the judges’ verdict remains that he was responsible for planting the bomb.
When asked for a verdict on Fhimah, Lord Sutherland replied ‘‘not guilty’’.
It took less than two minutes to read the verdicts.
Sentence on Al Megrahi will be announced at 1pm UK time.
After the reading of the verdict, a hush descended on the court as the clerk recorded the verdict, but there was no immediate word of the reaction in the crowded public gallery.
Dozens of relatives from Britain and US were in the courtroom, as well as several relatives of the two defendants.