The UK routinely extradites people to the US (and facilitated extraordinary renditions from UK soil). The claim he could not leave the UK for fear of being extradited to the US was always a nonsensical lie.
(there was no claim that the UK does not extradict to the US in general, but in this specific case they might not)
He is on his way to US soil right now and will appear in US territory before a US judge, he has been extradited.