Former Weakest Link star Robinson, 77, joined the Channel 4 quiz show last year, becoming its sixth presenter and the first female to take the role.
Robinson, who recorded 265 episodes of the show, said: “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.”
She added: “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.
“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.”
She will appear in shows until the summer with a new host announced in due course, Channel 4 said.
A show spokesperson said: “Quick-witted Anne has been a brilliant host on this iconic show.”
Robinson followed in the footsteps of Richard Whiteley, Des Lynam, Des O’Connor, Jeff Stelling and Nick Hewer as the presenter of Countdown, which launched in 1982.
She joined the daytime show last year alongside mathematician Rachel Riley and lexicographer Susie Dent, with her first instalment broadcasting on June 28.
In November 2021 Riley dismissed reports of a “feud” between her and co-star Robinson, telling ITV’s Lorraine: “You know not to believe tabloids. I think it is just you have got some women there now so they want to make something up.
“I have seen all the headlines of the feuds escalating. I have been on maternity leave for about six to eight weeks or something.”
Robinson became known for delivering cutting remarks to contestants when she presented The Weakest Link, which was first broadcast in 2000 before ending 12 years later at the peak of its ratings.