The comedian, who has hosted the show for nine years and chaired over 220 episodes, will leave at the end of the upcoming series, which begins on 15 May.
During her time as host, the programme has become one of the most popular on BBC Radio 4, attracting millions of listeners each week and regularly topping the list of most-requested radio shows on the BBC iPlayer.
Toksvig, who first appeared as a panellist in 1992, said: “The News Quiz is one of the things I am proudest of in my professional life. From the beginning when I arrived as a rather nervous panellist almost a quarter of a century ago, I have always enjoyed it and was overwhelmed when asked to become host back in 2006.”
“Now I have decided it is time to move on and of course I feel sad but I think it’s the right moment. 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.”
The comic, who has also written numerous books and plays, said she hope to one day return to The News Quiz and “muck about a bit?”
The award-winning broadcaster will make her last appearance as host on June 26.
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The News Quiz has been running since 1977 and Radio 4 said it would “begin considering options in terms of the future host and make an announcement later this year.”
Guests who have appeared alongside Toksvig Sandi include Armando Iannucci, Jeremy Hardy, David Mitchell and Jo Brand.