Robinson, 35, admitted the charge and received a 13-month jail term in May over footage he filmed outside Leeds Crown Court during a trial.
At the Court of Appeal, Lord Chief Justice Lord Burnett ruled there had been technical flaws by the judge who jailed him and quashed the finding.
Robinson's solicitors said everyone has the "right to a fair hearing".
Robinson, from Luton, whose real name is Stephen Yaxley Lennon, was not present for the ruling in London and is expected to be released from prison later.
In his written judgement, Lord Burnett said: "We are satisfied that the finding of contempt made in Leeds following a fundamentally flawed process, in what we recognise were difficult and unusual circumstances, cannot stand.
"We will direct that the matter be reheard before a different judge."
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