Supporters in the packed courtroom broke into a round of applause as Lord Burnett announced the decision.
Lord Chief Justice Lord Burnett and two other judges in London quashed a finding of contempt made against Robinson at Leeds Crown Court in May when he was sentenced to 13 months in jail.
Announcing the decision on Wednesday, Lord Burnett said the court was allowing his appeal “in respect of the committal for contempt at Leeds Crown Court”.
He added: “The appellant is granted bail and the matter of contempt at Leeds Crown Court is remitted to be heard again.”
The judges had been urged to overturn two contempt of court findings against Robinson, 35, whose real name is Stephen Christopher Yaxley-Lennon – made at Leeds Crown Court and at Canterbury Crown Court.
Supporters in the packed courtroom broke into a round of applause as Lord Burnett announced the decision.