The television personality revealed the surprise to viewers through a game of Hangman.
People at home called in to the show to offer up letters as part of the game, until the word “eggheads” was complete.
Absolutely Fabulous star Joanna Lumley appeared on-screen and said: “Jeremy’s big announcement is that Eggheads is coming back.”
Vine said: “The programme which I’ve 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.”
Prospective contestants were also encouraged to apply to be on the programme during Mr Vine’s show.
In a statement, Mr Vine added: “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 on Channel 5.”
Channel 5 commissioning editor Daniel Pearl said: “I’m delighted that Eggheads, one of the UK’s most loved quiz shows, has found a brand new home on Channel 5.
“This is yet another step in the transformation of Channel 5 as it grows its audience rapidly.”
A BBC spokesman added: “We sometimes have to make difficult decisions in order to grow new shows and 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.”
The programme began in 2003 and current host Jeremy Vine joined the programme in 2008.
The quiz show sees teams of contestants try to beat a panel of specialist quizzers in a test of their general knowledge.
£75,000 is the most money ever won by a team challenging the Eggheads.
Oxford Brookes University students Beer Today, Gone Tomorrow went down in history when they won the prize in 2007.
The news comedy show, which also featured comedian Rachel Parris, ran for four series and covered political issues such as Brexit, as well as the Conservative Party.
A spokeswoman said the show had been taken off air “to make room for new comedy shows.”
“We are very proud of The Mash Report but in order to make room for new comedy shows we sometimes have to make difficult decisions and it won’t be returning,” the statement said.
“We would like to thank all those involved in four brilliant series and hope to work with Nish Kumar, Rachel Parris and the team in the future.”