The dramatic creation by Philip Treacy has been likened to a Turkey Twizzler, a lavatory seat and a pretzel.
The 22-year-old princess wore it to the wedding of Prince William and Kate Middleton last month, and a Facebook page was set up in its honour.
The auction on eBay ended on Sunday, with the proceeds going to charities Unicef and Children in Crisis.
The identity of the winning bidder has not yet been revealed.
The princess commented on the auction page: "I've been amazed by the amount of attention the hat has attracted.
"It's a wonderful opportunity to raise as much money as possible for two fantastic charities.
"I hope whoever wins the auction has as much fun with the hat as I have."
Princess Beatrice's royal wedding hat has been sold on auction site eBay for £81,100.01.