The presenter, who has fronted the show for 10 years, will host his final episode on 19 December.
He is not leaving the BBC and will continue commentating Eurovision, judging on Drag Race UK and hosting his weekly chat show on BBC One.
Norton said he was "sad to be stepping away" from Radio 2, adding that he will "miss the listeners and their lives".
It has not yet been announced who will replace him on Saturday mornings.
Norton took over the slot from Jonathan Ross, who left the BBC in 2010.