Winkleman, currently pregnant with her third child, stepped down from her role hosting the BBC Two spinoff earlier this year.
Ball, who placed third in the 2005 series of the dancing competition, admitted that she is "quite literally beyond elation" to have won the role.
"There has been quite a hullabaloo at home with the news," the presenter said. "I'm giddy with glee and I may even have slipped momentarily into a celebratory cha cha cha, although technically not a very good one!
"Having been a contestant myself and having hosted the Strictly Come Dancing Tour, it would be fair to say I'm obsessed with the whole dance phenomenon. I love everything Strictly, from watching the partnerships blossom and bloom to the tricky footwork, the frocks and the shock exits, and of course the judges."
The 40-year-old, who currently hosts Radio 2's early Saturday morning breakfast show, added: "Physically and metaphorically I may have trouble fitting my huge feet into Claudia's tiny wee shoes, she is one fabulous lady, but I will do my best to bring all the ups and downs and laughter and tears behind the nation's favourite show to the fans. I can't wait to start this thrilling adventure. Such fun!"
Moira Ross, Strictly Come Dancing's executive producer, commented: "Zoe is a fantastic presenter and I'm delighted that she is joining It Takes Two. With her first-hand experience of the series, she's the perfect person to give viewers all the insider knowledge, gossip and news from this year's show."
Ball was previously reported to have screen-tested for the job alongside Denise Van Outen and Natasha Kaplinsky.
It Takes Two will return in its regular weekday slot later in the autumn.
> 'Strictly' replaces Jared Murillo with Pasha Kovalev