The 20-year-old from Lenzie, near Glasgow, is set to return as soon as it can be arranged by the authorities in Peru.
Scottish Prison Service (SPS) officials confirmed a deal had been struck after agreeing requests and conditions from the Peruvian authorities over the prisoner transfer arrangement.
It came as Peru accepted a request for the transfer of fellow drugs runner Michaella McCollum to a prison in Northern Ireland.
However, Reid and her family have been warned the process could take months - or even years.
Under Scots law, Reid - a first offender - would be entitled to see her sentence halved.
The pair - dubbed the 'Peru Two' - were held at Lima airport in August last year, after £1.5 million of cocaine was found in their luggage as they tried to board a flight to Spain.
A SPS spokeswoman said: "We have received application for the transfer of a prisoner and we have actioned the application.
"We await confirmation from the host authority as to when final transfer arrangements can be put in place."
It is understood once she is back in Scotland, Reid will be regarded as a 'low-risk' prisoner and could serve her time in a low-security facility.
She also could qualify for home leave, or even be released on an electronic tag.
The women protested their innocence for weeks, claiming they had been forced to smuggle the drugs by an armed gang.
However, they pled guilty in December in order to receive reduced sentences and were each jailed for six years and eight months.
In April, Justice Secretary Kenny MacAskill assured Reid's family he would give the move his backing - telling them: "She is one of us".
Both women are currently locked up in Lima's notorious Ancon prison after being transferred from Virgen de Fatima prison.
Reid submitted the prisoner transfer request after her parents paid a £3500 civil fine.
Reid was said to be "absolutely devastated" earlier this year after she had to miss her 22-year-old brother's wedding.