The 77-year-old TV presenter took over as the host of Channel 4's brainteaser quiz show in June 2021 but has announced she is stepping down after recording 265 episodes.
Robinson said in a statement: “I’ve had a blast hosting this wonderful show. And I stayed longer than I signed up for. Now it is time for an older woman to take the reins.
"I hope too I’ve encouraged TV bosses to realise that not all women at the wrong end of their seventies are in care homes playing bingo and watching conjuring tricks.
“In fact the genius of Countdown is that it’s a brilliant way to keep the brain exercised. I run 5k most days of the week.
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“And I can now do an anagram at twice the speed I could this time last year.
“But I have grandchildren, a large garden and a home in New York, all deserving more of my attention.”
Robinson will continue to appear in episodes until the summer and Channel 4 has said a new presenter - to join maths whizz Rachel Riley and dictionary corner lead Susie Dent - will be announced in due course.
A spokesperson for the show said: “Quick-witted Anne has been a brilliant host on this iconic show.”
Since Robinson joined the show there have been ongoing rumours of a rift between her and co-presenter Riley.
Countdown - a game of words and numbers - was first broadcast on Channel 4 in 1982, with Richard Whiteley hosting and mathematician Carol Vorderman assisting.
Since Whiteley's death in 2005, presenters have included Des Lynam, Des O'Connor and Sky Sports journalist Jeff Stelling.
Robinson replaced The Apprentice star Nick Hewer as host. He retired after 10 years at the helm.