Mr Burke had challenged the decision to move him, saying that the order committing him to prison in January specified Mountjoy.
The court heard last week that prison authorities decided to move Mr Burke because his enhanced prisoner status was removed from him due to his behaviour and he could not be safely housed in the general population.
The court was told Mr Burke's enhanced status was withdrawn due to his behaviour on an escorted trip to court.
Mr Burke has been in jail since January for contempt of court over his refusal to obey a court order to stay away from Wilson’s Hospital School.
In total he has spent more than 600 days in prison since September 2022, for refusing to agree not to trespass at the school.
He argued that legislation relied on by the prison service to justify his transfer did not apply to him as his was not a criminal case and he was not serving a sentence.
In his ruling this morning, Mr Justice Brian Cregan said Mr Burke had been ordered by a court to be detained in a prison. Even though he had been committed for civil contempt, the judge said he was a prisoner and legislation governing prisons applied to him. He said he was satisfied that he had been lawfully transferred from Mountjoy.
The judge said Mr Burke had come to court arguing that court orders were sacrosanct and must be obeyed by everyone and yet, simultaneously he was in prison for refusing to obey a court order.
'Everyone must obey court orders except him'
The judge said Mr Burke's view was that "everyone must obey court orders except him". The court order restraining him from trespassing was a lawful order of the High Court and it was not up to Mr Burke to decide if a court order was unlawful.
The judge said that was a matter for the High Court, Court of Appeal or the Supreme Court.
Mr Justice Cregan said Mr Burke may not like a court order or may not agree with it, but he had to obey it. He added that he was satisfied that Mr Burke knew full well the reason why he was in prison but still insisted on putting forward false reasons.
He said it may suit Mr Burke's political campaign against transgenderism - to pretend to the outside world and to his followers that he was in prison for his religious beliefs, but nothing could be further from the truth.
The court was not requiring him to "bend the knee to transgenderism", as Mr Burke had claimed, but simply to obey the order.
The judge added that Mr Burke had the "keys to his own prison cell" and could come to court at any time from Castlerea to purge his contempt.
The judge awarded the costs of the application against Mr Burke. Mr Burke argued no order should be made awarding costs against him - he said he had been moved with no warning and no notice. And he said prison authorities at the highest level had not been able to tell him whether or not the transfer was lawful.
However, the judge described Mr Burke's submission that he had not brought a formal motion before the court and that the court itself had "nursed" the application to court as ridiculous, and made the costs order sought by lawyers for the prison service.
The court will review the case again next month.