The song, about a Starman who would “like to come and meet us but he thinks he’d blow our minds” was released as a single in 1972.
It featured on the Ziggy Stardust concept album, which catapulted Bowie into international rock and pop stardom.
The handwritten lyrics, which were originally estimated to fetch up to £40,000, sold for five times more at £203,500 including buyer’s premium.
The winning bidder was Olivier Varenne, director of acquisitions and alliances and collections at the Museum of Old and New Art in Tasmania, on behalf of a private collector.
Paul Fairweather, of Omega Auctions, said: “We had almost unprecedented interest from around the world for this historic piece of memorabilia.
“We had five telephone lines in operation for the sale as well as bidders online and in the room.
“We’re very pleased with the incredible price achieved and are sure the lyrics will be rightly prized and treasured by the winning bidder.”
The lyrics were previously on display as part of the V&A Museum’s David Bowie Is collection, and they have been owned by the same person since the 1980s.
The A4 page features handwritten amendments and edits by Bowie, including corrected spelling mistakes and additions.
The lyrics were sold as part of a David Bowie and glam rock sale on Tuesday.
In 2019 the first demo of Bowie singing Starman sold for £51,000 after gathering dust in a loft for nearly five decades.
Bowie can be heard telling his guitarist Mick Ronson, who died in 1993, that he has not finished singing the song when he tries to end the demo.
The singer, born David Jones in post-war Brixton, died aged 69 on January 10, 2016.