The Lord Chief Justice, Lord Phillips, said his 2001 conviction must be quashed after hearing fresh scientific evidence.
It related to a single particle of firearms discharge residue (FDR) found in the pocket of George’s Cecil Gee overcoat a year after the murder.
Lord Phillips, sitting with Lord Justice Leveson and Mr Justice Simon, announced that the jury had been “misled” over the evidence relating to the particle.
Lord Phillips said: “It is impossible to know what weight, if any, the jury attached to the FDR evidence.”
He said the court had now been told it was “just as likely that the single particle of FDR came from some extraneous source as it was that it came from a gun fired by the appellant”.
Reading out a summary of the court’s decision, Lord Phillips said: “The prosecution called expert witnesses at the trial, whose evidence suggested that it was likely that the particle of FDR came from a gun fired by Barry George rather than from some other source.
“Those witnesses and other witnesses from the Forensic Science Service told the Court of Appeal that this was not the right conclusion to draw from the discovery of the particle of FDR.
“It was, in fact, no more likely that the particle had come from a gun fired by Barry George than that it had come from some other source.
“The Court of Appeal concluded that, if this evidence had been given to the jury at the trial, there is no certainty that they would have found Barry George guilty.”
It was George’s second legal challenge to an Old Bailey jury’s 10 to one majority verdict that he shot Dando.
He lost his first appeal in 2002 but his case was later taken up by the Criminal Cases Review Commission, an independent body which investigates possible miscarriages of justice.
Mr Justice Griffith Williams excluded the FDR from the retrial, agreeing that it was inconclusive.