Ministry officials said 10 detainees were turned over and the remaining 82 from Camp Bastion would be transferred "as soon as possible," the BBC reported.
Legal challenges are preventing the transfer of seven detainees. However, two men on Thursday dropped legal challenges to their detention and now may be transferred, the High Court heard.
The court confirmed, subject to detainees confirming they did not want legal representation, they could be transferred to the Afghan National Detention Facility, the BBC said.
Defense Secretary Philip Hammond said he was "very pleased" the High Court agreed to alter the ruling that held up the transfer of the suspected insurgents held at Camp Bastion.
"Terms have been agreed that will allow those detainees who have requested transfer to Afghan custody to be handed over," Hammond said. "Unfortunately, the injunction remains in place for some detainees who are still represented by human rights lawyers."
The BBC said seven other detainees would be contacted by their attorneys on whether they still want to mount a legal challenge.