Slater, 25, from Birmingham, had served more than two years after being arrested in January 1994.
Subsequent appeals for her release were dismissed, but Britain's former High Commissioner Sir Nicholas Fenn last year appealed for her to be pardoned. The request was followed up on a number of occasions by the British authorities in India and finally by the new High Commissioner, David Gore-Booth in June.
The Foreign Office said: "This is very good news for Samantha and her family. We worked hard for this and are grateful to the Indian authorities for this outcome."
Slater's mother Brenda said: "I can't believe my Sam is finally coming home. I won't have to spend another Christmas without her. She'll be the best present I've ever had. I just can't wait to give her a big hug."
During the period of her imprisonment in Trichur, in the southern state of Kerala, she was treated for a wide variety of complaints, including worms, dysentery and skin diseases.
She shared a cell measuring 15 sq ft with 12 other women, and lived on a diet of bread, rice and bananas. There were fears that her eyesight was starting to deteriorate.
Slater's ordeal began when she was arrested at a police road-block while travelling with a boyfriend in the mountains south of Goa.
She is believed to have been carrying less than an ounce of the drug (27 grams).Reuse content