BBC Two has screened The Simpsons for the past six years, but channel controller Jane Root pulled out of negotiations because she felt she was unable to justify spending licence-payers' money on a new deal.
Each episode has cost £100,000 to screen until now, but a bidding war - believed to still include Channel 4 and Channel 5 - has pushed the rate up to £700,000.
Sky One has had first rights to the show since it began on its sister Fox network in 1989, but BBC Two snapped up terrestrial rights in the mid-1990s.
Currently, the BBC has rights to show six of the 13 series of the cartoon, which features the comic misadventures of Marge, Homer, Bart and Lisa.
Those rights include three series which will be new to BBC Two, and the corporation can continue showing the programme until 2006.
But whichever channel wins the rights to series 12 will also be able to show repeats within a matter of months, and can start showing new episodes from 2004.
A BBC spokesman told BBC News Online: "Following vastly inflated bids from rival terrestrial channels, the BBC has decided to walk away from the negotiating table.
"Jane Root decided that like Premiership football, the cost of The Simpsons was too high to justify being paid for out of the licence fee."
As well as being one of Sky One's most popular shows, the Simpsons has also been a success for BBC Two.
It consistently outrated Chris Evans' TFI Friday on Channel 4 - even though the BBC's episodes had, at the time, been shown years before on Sky.
Newer episodes have been scheduled to run nightly to combat Channel 4's Superman prequel series, Smallville.