The 56-year-old will step down at the end of the upcoming series, which begins on Friday 15 May.
"I have decided it is time to move on and, of course, I feel sad but I think it's the right moment," said the host.
"The show is in great shape and, like a good house guest, you should always depart when people still wish you'd stay a bit longer."
Toksvig first appeared on the programme as a panellist in 1992, when the programme was chaired by Barry Took.
She took over at the helm in 2006, since when she has presided over more than 220 episodes.
In some recent editions, however, the Danish-British comedian was replaced by stand-ins Susan Calman and Jeremy Hardy.
A BBC press release said Toksvig had made the "difficult decision" to leave in order "to embark on a new and exciting stage of her career".
The News Quiz was created by producer John Lloyd in 1977 - before he went on to work on the likes of Blackadder, Not The Nine O'Clock News and QI.
Barry Norman was the first chairman, with Private Eye editor Richard Ingrams and Punch editor Alan Coren as team captains.
It is frequently among the requested radio programmes on BBC iPlayer; while a podcast edition, which alternates between The Now Show and The News Quiz, depending on which is currently on the air, has been downloaded 116 million times globally since its launch in September 2007.
Toksvig, who was made an OBE in the 2014 New Year's Honours, asked the Prince of Wales to appear on the show as he presented her with her medal.
After the investiture, she said: "I have spent too long making jokes to think that anybody would think that is worth rewarding - so I was honestly completely overwhelmed."
Gwyneth Williams, controller of BBC Radio 4, called her one of the station's "most talented and respected presenters".
"She will be hugely missed from The News Quiz and I want to thank her for her contribution over so many years. She brought her own inimitable wit, humanity and intelligence to The News Quiz - and above all that irresistible laugh."
A new host will be announced later this year.
Comedian Sandi Toksvig is to leave BBC Radio 4's comedy show The News Quiz after nine years and 28 series.