Sobhraj, 78, a French national, is suspected of killing more than 20 Western backpackers on the "hippie trail" through Asia, usually by drugging their food or drink in the course of robbing them.
He had been held in a high-security jail in Kathmandu since 2003, when he was arrested on charges of murdering American backpacker Connie Jo Bronzich in 1975.
Sobhraj denied killing her and his lawyers said the charge against him was based on assumption.
Several years later he was also found guilty of killing Bronzich's Canadian friend, Laurent Carriere.
But he was suspected of many more murders.
Thailand, where he was known as the "bikini killer", issued a warrant for his arrest in the mid-1970s on charges of drugging and killing six women, some of whom turned up dead on a beach near the resort of Pattaya.
He was, however, jailed in India before he could stand trial on those charges.
Nepal's Supreme Court on Wednesday ordered his release from prison, where he has served 19 years of his 20-year sentence, citing his age.
Sobhraj is expected to walk out of a high-security prison in Kathmandu on Thursday, his lawyer Ram Bandhu Sharma told Reuters.
He is expected to be taken to the immigration department to complete paperwork before being sent to France in the next 15 days, Sharma said.
Sobhraj was born to an Indian father and Vietnamese mother.
Associates have described him as a con artist, a seducer, a robber and a murderer.
He was also known as "the serpent" because of his ability to disguise himself following his escape from a prison in India in the mid-1980s.
He was later caught and jailed there until 1997.
He returned to France following his release in India but in 2003 was arrested at a casino in Kathmandu in connection with the 1975 murders of Bronzich and Carriere.
Last year, the BBC and Netflix jointly produced a TV series dramatising his crimes called The Serpent.
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