As part of the revamp Keaveny will move to the flagship 7am to 10am breakfast show, from his Saturday evening slot next month while Jupitus, who is a team captain on BBC Two's 'Never Mind the Buzzcocks', will leave the station to concentrate on his stand up comedy.
Lesley Douglas, controller of Radio 2 and 6 Music, said: "I have long admired Shaun Keaveny, his irreverence, humour and love of music will make his the perfect new breakfast show presenter."
Douglas also said that the door has been left open for Jupitus to return to the station in another role.
Keaveny joined BBC 6 Music last year from GCap Media's Xfm, where he presented the Friday breakfast show.
As well as Keaveny's promotion 'The Queens of Noize' show, featuring Mairead Nash and Tabitha Denholm, will be moved from its Saturday night slot to Saturday afternoon.
George Lamb, is to present the 'Dream Ticket', Monday to Thursday 10pm to 1am slot, which features music from the BBC archive mixed with new material and listeners' gig reviews.
In addition film maker and musician Don Letts will host a new show on Friday nights while Guy Garvey, lead singer with Manchester band Elbow, is to join the station taking the 10pm to midnight slot on Sunday evenings.