The pair have worked together for the past eight years, becoming a popular feature on Radio 1 because of their wit, satirical humour and affection for causing mischief.
Until September this year, JK and Joel had been presenting the 'Early Breakfast Show' on BBC's Radio 1 from Monday to Friday, warming up the audience for the 'Breakfast Show' with Chris Moyles. Since September they have been filming their TV shows, such as the BBC's 'Hider and the House', ITV's 'Sing it Back: Lyric Champion' and Five's 'Worst Celebrity Driver'.
They have also presented Radio 1's 'The UK Chart Show' and appeared on a number of celebrity reality TV programmes.
JK and Joel said in a joint statement: "No longer are we hauling our arses out of bed at 3am looking like crap, instead we are really looking forward to doing weekends.
"It'll be great to go up against our old mate Vernon at 10am, that's if he can be bothered to turn up -- his random gameshow schedule is demanding, don't you know."
This is the latest signing by David Lloyd, the new Virgin Radio programme director, who recently appointed former LBC presenter Iain Lee to present a Sunday night show between 10pm and 1am. Lee's first show will air on January 6.
Lloyd said: "JK & Joel love radio -- that's why they are joining us. Virgin is a place where they can have some fun. This signing, coupled with Iain Lee's, signals what our new weekends are about."
The boys replace DJ Leona Graham, who is expected to stay with Virgin in a new role, which is still to be confirmed.