A spokeswoman refused to comment on why they won't mount a challenge, saying: "We won't be commenting on that at this stage."
Watson's lawyer Kerry Cook said they were happy with the judge's ruling and would now await Corrections decision on how the visits would work.
It's understood that conditions and details of how the visits will work are yet to be fleshed out by Corrections bosses.
While Justice Dunningham said there was "no rational basis for declining a face-to-face interview between Mr White and Mr Watson", there may be conditions, particularly as to the format of the interviews, and controls on the distribution of any recorded materials, that the chief executive of Corrections may wish to impose when revisiting the decision.
Watson is currently serving a 17-year sentence for the 1998 New Year's Day murders of Ben Smart and Olivia Hope in the Marlborough Sounds.
He was denied parole last month.