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.
At a hearing in July, his QC Jeremy Dein argued that procedural “deficiencies” had given rise to “prejudice”.
Mr Dein also submitted that the sentence was “manifestly excessive” and that “insufficient” regard had been given to personal mitigation.
Robinson was jailed in May after he filmed people involved in a criminal trial and broadcast the footage on social media.
The footage, lasting around an hour, was watched 250,000 times within hours of being posted on Facebook.
The far-right activist was given 10 months for contempt of court, which he admitted, and a further three months for breaching a previous suspended sentence.
Robinson was detained outside Leeds Crown Court after using social media to broadcast details of a trial which is subject to blanket reporting restrictions.
It was the second time Robinson had breached court orders, having narrowly avoided jail in May last year over footage he filmed during the trial of four men who were later convicted of gang-raping a teenage girl.
The judge on that occasion gave him a three-month suspended sentence and told him his punishment was not about “freedom of speech or freedom of the press” but about “justice and ensuring that a trial can be carried out justly and fairly”.
Mr Dein argued during the recent appeal proceedings that the findings of contempt of court on each occasion should be quashed as a “conglomeration of procedural deficiencies” had given rise to prejudice.
The QC said the proceedings in Leeds had been “unnecessarily and unjustifiably rushed”.
He told the judges: “We maintain it is of particular importance that right from the outset the appellant, albeit in a very stressful and difficult situation, offered to have the live stream taken down and contact people who could do so.”
There had been no intention to disrupt the trial or to breach any order, Mr Dein said.
The Court of Appeal judges announced that they were dismissing Robinson’s appeal in respect of the earlier contempt finding at Canterbury Crown Court.