The Dallas Safari Club in Texas says the hunt will help protect the species by removing an old aggressive rhino, and funding future conservation.
However, the auction has been fiercely criticized by conservationists, and has even drawn death threats.
Namibia is home to about a third of the world’s 5,000 black rhinos, and issues just three hunting permits a year.
It is the first time a permit has been auctioned outside the southern African nation.
The auction was held amid tight security at a Dallas convention centre, where dozens of protesters had gathered.
The winning bidder – who has not been named – will hunt an old, non-breeding male rhino.
The organizers say such animals actually pose a threat to younger rhinos, which they sometimes charge and kill.
All proceeds will be donated to the Namibian government and will be earmarked for conservation efforts, safari club officials said.
Animal rights groups described the hunt’s conservation claim as “a sad joke”.
“This auction is telling the world that an American will pay anything to kill their species,” Jeffrey Flocken of the International Fund for Animal Welfare (Ifaw) told the Associated Press.
“This is, in fact, making a spectacle of killing an endangered species.”
More than 80,000 people signed online petitions against the auction.
The FBI says it is investigating a string of death threats over the auction.
At present it is estimated that there are around 20,000 white rhinos left.
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