Melissa Reid and Michaella McCollum's hopes of a swift return to the UK were bolstered after British embassy officials in Lima visited them in jail to tell them their transfer request had been accepted.
Peruvian authorities must now sanction the move before they are transferred to their home country to serve out the rest of their six year and eight month prison sentences.
A Lima source said last night he expected the process to take around six months but they could be on a plane back to Britain in three months if there were no bureaucratic 'hold-ups'.
State prosecutors, a judge and two government ministries in Peru will now be asked to rubber-stamp the transfer.
Reid, 20, from Lenzie, and McCollum, 21, from Dungannon, Co Tyrone, were caught with the haul at Lima airport on August 6 last year. They were working on the Spanish party island of Ibiza when they claimed Colombian drug lords, who kidnapped them at gunpoint, forced them to board a flight with 24lb of cocaine in food packets hidden inside their luggage. They had faced the prospect of a maximum 15-year prison term but struck a behind-closed-doors plea bargain to secure a shorter sentence.
The Scottish Prison Service (SPS) said it has approved a repatriation application it received from Lima earlier this year.
Prison chiefs are now waiting for the Peruvian authorities to agree on the terms of the transfer before it can take place.
A SPS spokeswoman said: "We have provisionally given consent to the Peruvian authorities for the application."