"In her summary the judge notes that, 'The investigation was fair and the report is without error," Smith said.
"There is now a period in which the parties have the opportunity to consider the judgment and as such I do not intend to make any public comment on this in the interim.
"I must consider when and in what form the [chief inspector's] report is to be released to ensure any security and privacy issues are managed which is why I will be consulting with the Office of the Ombudsman."
Serco was seeking an order that before the chief inspector's report was released, it was revised to "provide a fair and accurate account of the situation at Mt Eden".
Serco Chief Executive Mark Irwin said the company noted the decision and accepted it.
"We have always accepted the recommendations of the report, but brought the proceeding because we had genuine concerns about the process.
"We have acknowledged that under our management, following a period of good performance, standards in Mt Eden slipped in early 2015, and we have apologised for this."
Serco was supporting Corrections' management of Mt Eden by providing staff and other transition resources, Irwin said.
It continues to manage the Wiri Prison in South Auckland and that had been operating well, he said.
"All prisons have to deal with challenges, and we are grateful for the partnership of the Department as we work together to address them."
Serco had been in charge of Mt Eden prison since 2011, having won a $300 million, 10-year contract.
In April, the Government announced it has charged Serco $8 million to cover the costs of resuming control of the prison.