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.
"Obviously I'm sad to be stepping away from my Radio 2 show," he said in a statement.
"I'll miss being a part of the Wogan House family, as well as the listeners and their lives. I'd like to thank my producer Malcolm Prince and all the teams I've worked with for a great decade of radio.
"Happily with the chat show, Eurovision and Drag Race the BBC continues to be my perfect TV home."
Norton's guests on his Radio 2 show over the last decade have included Olivia Colman, Kylie Minogue, JK Rowling and Tina Turner.
Regular features include the agony aunt slot Grill Graham, with co-presenter Maria McErlane, and his pick of a cheesy song of the week, I Can't Believe It's Not Better.
Charlotte Moore, the BBC's chief content officer, said he would be "hugely missed on Saturday mornings on Radio 2".
"He is a first class broadcaster but I'm thrilled he's committed to continuing to be a regular fixture on the BBC," she added.
Helen Thomas, Head of Radio 2 said: "For the past decade, Graham has made Saturday mornings his own on Radio 2.
"His sparkling interviews, as well as his brilliant shows from the Eurovision host city each May, have kept millions of listeners entertained each week."