Mark Paterson, 55, was convicted of sexual assault on a woman at Aberdeen University chaplaincy following a five-day trial in 2006. He was ordered to carry out 200 hours' community service.
His case was referred back to appeal judges in 2012 by the Scottish Criminal Cases Review Commission, which was set up to investigate alleged miscarriages of justice. This was because of potential fresh evidence that did not feature in the trial.
Lady Smith, who heard the appeal with Lady Dorrian and Lord Philip, overturned the conviction following evidence at the Justiciary Appeal Court in Edinburgh.
Mr Paterson, a Carmelite friar, said: "I am delighted. I am over the moon."