It is not clear if her co-host, Noel Fielding, will continue presenting the popular cookery show in her absence. He posted he how he would: "miss Sandi and our strange and magical double act."
In a statement released on Thursday morning, the star said: "When stepping down from a job it is quite common for people to say they are doing so in order to spend more time with their family.
"Unusually, I am departing from the Great British Bake Off so I can spend more time with my other work."
She continued: "As my waistline will testify, Bake Off is an all-consuming show.
"Spending time with Prue, Paul and Noel has been one of the great pleasures of my life.
"These are friendships which I know will continue beyond the confines of television.
"Bake Off is a wonderful programme which has already proved it can happily withstand a change of hosting personnel.
"The reason for that, of course, is that the true stars of the show are the bakers themselves.
"I wish everyone well."
Her co-hosts shared their sadness in the wake of the announcement.
Noel Fielding led tributes, "I feel like Tom without Jerry! Mick without Keef! I’m gonna miss you Sandi and our strange and magical double act. It’s been a joy to hang out and muck about in the tent with you. Thank you for three wonderful years! You will always be my favourite Ewok Viking!"
Prue Leith, who works as a judge on the show, tweeted: "I have absolutely loved working with Sandi, she's been a brilliant host and enormous fun and I am in awe of how hard she works juggling so many different projects. We shall be lifelong friends' way beyond the tent."
Paul Hollywood also paid tribute to Toksvig: "It's been great fun working with Sandi. We will miss her but I hope that she will get time to visit us in the tent when we film later this year. She will always be part of the Bake Off family."
Fans have been left "disappointed" by the presenter's announcement.
One wrote: "This is a shame, she’s fantastic on the programme. Her and Noel are fabulous together."
Another added: "What a blooming shame, Sandi and Noel make a superb team."
Channel 4 said her departure would leave fans missing her "warmth and wit, not to mention her endless willingness to be the butt of jokes."
The broadcaster said she will continue to engage with its programmes on a series of new shows in development, although it added "none of these involve cake".