Describing her 21 years on the show, Daly said it was "hard to put into words" what the experience had meant to her.
"Strictly has been more than just a television programme. It's felt like having a third child, a second family, and a huge part of my life since that very first show.
"I knew then it was something special, but I could never have imagined the magic it would bring."
She also paid tribute to "the incomparable Sir Bruce Forsyth", saying: "Brucie set the tone for everything that Strictly became: warmth, wit, connection, and pure showbiz magic."
Winkleman, who also hosts Celebrity Traitors, added: "Strictly is a magical, glittery, fake-tanned train and it's been a privilege to be a tiny part of it.
"It has been my everything, the show I will be eternally grateful for.
"I will never forget Len Goodman trying to teach me what a cucaracha is (I still don't know) and the complete thrill and honour it was to work with Tess on the results show to co-hosting on Saturday nights."