The chef is the fourth contestant to be confirmed for the forthcoming BBC One show and follows in the footsteps of boxer Nicola Adams, who last year danced in a partnership with professional Katya Jones.
The news was announced by guest presenter Matt Lucas on BBC Radio 2 during the Zoe Ball Breakfast Show.
The cookery author said he is "very, very nervous" about taking part, but told programme host Lucas: "It's an honour. When they asked me if I'd be interested, I just bit their hand off because I thought, you know, to do that and represent the LGBTQ+ community is one thing, but also just to see two men or two women dancing together is not necessarily about sexuality, it's just about intimacy and respect.
"And I think that's going to be such a great thing in our culture, where men are sort of conditioned not to open up and not to be emotional, I think it might help to combat that.
"So I'm excited on so many levels to be doing the first all-male partnership. I don't think it's quite sunk in yet."
Speaking about the all-male pairing, Lucas commented: "As a kid, I never would have dreamed that that sort of thing would be possible."
Whaite said he hopes "kids watch this and see it and it becomes normal for them, they don't have to grow up in shame.
"They don't have to grow up worrying about who they are. I hope this kind of sets a bar for kids to think: 'I am who I am and I'm proud of that.'"
He won the third series of The Great British Bake Off in 2012 and currently presents a weekly cooking segment on the Channel 4 show Steph's Packed Lunch.
In a message posted on his Instagram stories, Whaite thanked everyone for the "overwhelmingly kind messages".
He added: "I'm turning my phone off for a little while just to process it all.
"I'm very excited, very nervous, but most importantly very honoured to be able to show the next generation that being yourself is what matters the most in life."
Following the announcement on air, he said in an official statement: "I'm so grateful, excited, and nervous to be joining the Strictly 2021 family.
"I've been wearing sequins and jazzy attire since I was three years old and can't wait to hurl myself, full throttle, around the most glamorous dancefloor on earth.
"What's more exciting for me is that I'm going to be one half of the first all-male partnership, which is a great step forward in representation and inclusion.
"Whoever it is I'm paired with, I hope they are up for a challenge as I want our routines to include lots of spectacular lifts!"
His professional dance partner has not yet been confirmed, but the cooking star said given he is 6ft 2in it would need to be someone tall.
University Challenge star Bobby Seagull was among the people congratulating Whaite.
He tweeted: "Well done John. I've been looking forward to seeing a Bake Off star on the dance floor!”