Daily mail has a headline that it's based on the promise that he won't be held at one of the supermax prisons. Does not sound very convincing. The us still has Guantanamo and black sites around the world.
It is; the reason the original decision was overturned is that specific formal 'assurances' have been received from the US government which mitigate the suicide risk which was the only reason the first instance judge refused admission.
The reason the assurances are trusted is that the US has never been found to break the letter of these assurances in the past. (The appeal judgement does note that where the assurances are loosely worded, the assumed spirit of them have not always been followed).
Bizarrely, these kind of inter-state promises of special treatment are a common part of global extradition practice.