Coulson, who went to on become David Cameron’s comms director after leaving the newspaper, was alleged to have lied about his knowledge of phone hacking at the News of the World.
However, Judge Lord Burns said it had not been demonstrated that Coulson's evidence was relevant in the Sheridan trial.
Speaking to reporters after his acquittal, Coulson said the "right decision" had been made, adding that he "didn't lie".
He was charged three years ago after being questioned in Glasgow in connection with his evidence to the Tommy Sheridan trial in 2010.
Sheridan was found guilty of perjury and was sentenced to three years in prison in 2011. Officials at the Crown Office in Edinburgh waited for the outcome of Coulson’s trial in England before announcing any action against him.