Reid and her accomplice Michaella McCollum, from County Tyrone in Ireland, were jailed for more than six-and-a-half years after being caught with 24lb of cocaine in their suitcases at Lima International Airport in August 2013.
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McCollum was freed in March under new legislation on early prison release.
The Foreign Office confirmed Reid’s expulsion.
The 22-year-old from Lenzie, Scotland, has served about one third of her sentence, and because she has obeyed the system and met the legal requirements to be released, she will be returning to United Kingdom soon.
Last month the UK’s Foreign Office said a judge in Peru would rule whether Reid should be expelled from the country “in the next few days”.
A Peruvian court on Thursday said Reid has shown remorse for the crime, and authorities agreed to release her. She has also paid a fine of 10,000 Peruvian soles, just over £2,000.
McCollum got out on probation last April but has been ordered to remain in the country until completing her sentence in 2020. However, she is likely to stay in Peru for lengthy period in order to execute her parole conditions.
The 22-year-old was jailed for cocaine smuggling in 2013 and had appealed to be expelled to serve the remainder of her sentence closer to home.
They had claimed they were forced to carry the drugs, but pleaded guilty to charges later that year.
They said she had met the legal requirements to be released because she had complied with other measures.
Customs discovered 24lbs of the drug in food packages hidden in their luggage.
Reid’s father Billy has previously said the impact of his daughter’s imprisonment on his family had been “horrendous”.
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The statement said Peru’s National Migrant Agency, the British embassy in Lima and the prisoner will be notified prior to “proceeding to a transfer to her home country”.
