First airing in 2003, the series has since seen over 1,800 episodes on the BBC.
Current host Jeremy Vine will follow the show over to its new home on Channel 5.
"The programme which I presented for more than 10 years, Eggheads, one of the greatest quizzes in the history of British TV, is moving to Channel 5 later this year," he said.
"I can’t wait to be reunited with the mighty Eggheads and see new teams try to take them on
“I’m sure fans of Eggheads will share in my delight that it has found a new home."
The BBC said: "We sometimes have to make difficult decisions in order to grow new shows.
"We would like to thank the Eggheads and host Jeremy Vine for their time on the BBC and wish them well with their next chapter."
Judith Keppel, one of the Eggheads, said: "I'm thrilled to bits, I can't tell you how lovely it will be to have something to do at last!"
Other Eggheads are Kevin Ashman, Chris Hughes, Barry Simmons, Pat Gibson, David Rainford, Lisa Thiel, Steve Cooke and Beth Webster.
They're all expected to reprise their roles when the series starts on Channel 5 later in 2021.
Eggheads previously aired weeknights at 6PM on BBC Two.
The format sees one group of contestants attempt to win a cash prize against a team of the Eggheads, with the prize pot increasing each game until the Eggheads are beaten.
The biggest prize won to date has been £75,000 while almost £2 million in total has been paid out since the first episode aired.
Alongside the main show, there have been a number of spin-offs over the years.
These have included a Celebrity series, Are You an Egghead?, Revenge of the Egghead and Make Me an Egghead.