The announcement by the BBC ends weeks of speculation prompted by Sir Bruce's decision to step down from the show after a decade.
Daly and Winkleman were strongly fancied to land the permanent slot together after impressing viewers with their on-screen chemistry in the weekly results show and during Sir Bruce's occasional absences.
The pair will take over in the autumn when the series returns, with Daly switching to Sir Bruce's usual position introducing each of the dances and probing the judges for their reactions.
Winkleman, who will be upstairs hosting the post-dance interviews, said: "I have loved Strictly since the second it appeared on our screens and I am honoured and thrilled to now be part of the Saturday night team.
"Working alongside Tess is always fantastic and I can't wait to spend the weekends with her, our amazing dancers and the greatest judging panel on the planet. Sir Bruce is a living legend and we'll all miss him very much."
Daly said: "I'm so pleased that I'll be working with Claudia - she's long been part of the Strictly family and I've loved doing the Sunday show with her.
"It's really exciting having two women host the show, and we are great mates so there'll be lots of fun to be had on and off the dance floor, and of course I'll look forward to being reunited with Brucie for the Children In Need and Christmas shows."
Programme judge Bruno Tonioli recently declared he would love to see the duo given the role, when he said: "I'll be delighted to have Tess and Claudia - they are fantastic, they work very well together."
Show bosses are currently in talks to finalise the line-up for the professional dancers.
Charlotte Moore, the controller of BBC1 said: "Tess and Claudia are a fantastic duo and natural successors to Strictly's presenting line up now that Sir Bruce has decided to step down.
"Their commitment and passion for the show make them the perfect pairing to take Strictly into a new era."