The judgement found that the decision to refuse Anderson's request was based on inaccurate information about the risk he posed.
The decision had been taken by the duty governor at Maghaberry Prison.
In his judgement, Mr Justice Rooney found that an internal assessment of Anderson's likelihood of reoffending had been recorded at a higher level than the score held on the Prison Service's internal system.
A legal representative for the Prison Service told the court that the increased score had come from a colleague rather than the duty governor's personal knowledge.
When the system was checked, Anderson's score was 27, indicating a medium likelihood of reoffending, rather than 32, which had been recorded as a high likelihood in the decision letter.
The judge found that the duty governor "clearly took account of this incorrect information" when assessing the risks and considering whether the decision was proportionate.
There is a question mark about what happened after the judge knocked back the original decision.
According to the judgement, the judge invited the duty governor to reconsider the decision, but that offer was declined.
The judge described the decision not to review it as "somewhat surprising" and he granted Anderson temporary release subject to a number of conditions, finding that the Prison Service's decision was "flawed" and had taken into account "irrelevant and incorrect factors".
The judge said the failure to secure and take account of the correct risk assessment was unlawful.