She joked: "I haven't danced since I was seven and Miss Beer sent me home from my ballet class because I was hopelessly uncoordinated."
Rice will join a host of actors, comics, sportspeople, and YouTubers in hitting the famous dancefloor.
The search for the 17th Strictly winner will begin with a launch show on BBC One in September.
Rice, who was announced on Steve Wright's Radio 2 show on Wednesday afternoon, rose to fame on Channel 4's Bafta-nominated game show Treasure Hunt in the early 80s, before being given her own BBC One show, Challenge Anneka.
The show, which ran from 1989-95, found Rice being tasked with completing a randomly set challenge within a certain time frame, which should bode well for her time on Strictly.
"My family and friends haven't seen me dance since, not at a wedding or round a handbag so it's going to be a challenge for my partner," she added.
"In fact I've asked for two, one on each side. I can't see myself in a long frilly dress either. But I'm feeling recklessly excited. Strictly has always been my autumn's entertainment and now I'm part of it! My children will probably leave the country".
More recently, the 60-year-old has appeared on Celebrity Mastermind and Come Dine With Me, as well as Celebrity Hunted alongside fellow dancer Jamie Laing.
Earlier on Wednesday, Olympic rower James Cracknell promised to bring some "dad dancing" to the show early on.
Cracknell was made an OBE in 2005 after winning gold in the coxless fours at the 2000 and 2004 Olympics.
Speaking on Good Morning Britain about his dancing style, the 47-year-old said he liked to "single-mindedly lean on a bar and at a certain point in the night think 'I'm really going to dance'".
The oarsman, who rowed for Cambridge in this year's Boat Race, added: "It's going be really interesting having no confidence in it and then going 'OK, can you do it?'"
In the official Strictly press release, Cracknell joked he was looking forward to taking part "having spent so many years mucking around in a rowing boat with big men in tight lycra," and that "it's time I learned a new skill.
"I need to apologise to my kids in advance for the embarrassment."
Late on Tuesday, Radio 1 DJ Dev Griffin - who presents the afternoon weekend show on Radio 1 alongside Alice Levine - became the 13th contestant known to be limbering up for the dance show.
He revealed he came second in a dance competition at a Pontins holiday park in 1996, when he danced to MC Hammer's Can't Touch This.
Griffin was a finalist on 2017's Celebrity MasterChef and has appeared on other celebrity versions of popular programmes, such as Mastermind. He's vowed to improve on this by winning Strictly.
Announcing the news on Radio 1, he said: "I am really good at dancing. I never had any formal dance training, but I am pretty good, I have made myself good.
"All I want is to win. I don't believe in doing things for taking part, if you are going to do something, you do it to win."
Image copyrightGETTY IMAGES
Earlier on Tuesday, Alex Scott was also confirmed as a contestant for Strictly Come Dancing.
The former Arsenal and England footballer said she "felt like a kid at Christmas" after her participation was revealed by DJ Ace on Radio 1Xtra.
Scott, who is now one of the country's leading pundits, won the Strictly Comic Relief special in 2018.
"This is a show that I've always wanted to be a part of," Scott admitted. "When I did [Comic Relief], I was like 'I want to be part of the main one.'
Former Lioness Scott out-danced fellow ex footballers Chris Kamara and David Ginola en route to winning the 2018 Comic Relief Strictly special, alongside dance partner Pasha Kovalev.
On Monday, Made in Chelsea star Jamie Laing joined the line-up. "I think I've got a little bit of rhythm," he told ITV's Loose Women. "We're going to find out."
The reality TV star, who was persuaded to demonstrate his credentials by performing "the worm" in front of the Loose Women panel, said he'd known for a month about his participation but had to keep it a secret, even from his own mum.
"At last she'll be proud of me!" he joked.
Earlier, Seduction singer Michelle Visage - best known for her role as a judge on the US reality TV show RuPaul's Drag race - was also revealed as a contestant.
"Who's ready for our next RuVeal?" tweeted the official Strictly account.
"She's here to to slay the ballroom..."
A 10th contestant was revealed in the form of table tennis Paralympic champion Will Bayley.
Bayley, who is ranked world number one, took gold for Great Britain at the 2016 Summer Paralympic Games in Brazil.
"I'm so proud to be on the show, it's my family's favourite show," he said.
"I have no dance experience at all, but I hope I can do well. I want to inspire people with a disability - that would mean a lot to me. I want to prove to people I can do this."
Laing, Bayley and Visage come hot on the heels of Emma Thynn, Viscountess Weymouth, who was announced on Sunday.
The 33-year-old chef and model is a contributing editor for British Vogue and also runs Longleat safari park with her family.
Viscountess Weymouth - who married Ceawlin Thynn, Viscount Weymouth, in 2013 - was unveiled as a Strictly contestant on BBC Radio London.
The mother of two told host Gaby Roslin: "It's so, so exciting, it's such an institution."
She added that she had never danced professionally but that she was sure it would be "such an amazing experience from start to finish".
CBBC presenter Karim Zeroual has also been confirmed for the dancefloor.
The former child actor who starred in CBBC's The Sparticle Mystery said he was "pinching" himself after being offered the chance to take part in the programme
He said: "I want the lot. The skimpiest of clothes, the widest of flares, the brightest of colours and the tallest Cuban heels a guy can find! The more flamboyant the better... sequins galore please!"
BBC sports news presenter Mike Bushell said being revealed as a Strictly contestant felt "like a weird dream" but he wanted to fly the flag for "all the dad dancers".
The 53-year-old added he "thought they'd got the wrong person," when he got the call from the producers, as people frequently confuse him with former BBC colleague and 2009 Strictly winner, Chris Hollins.
Former Coronation Street actress Catherine Tyldesley is also dusting off her dancing shoes.
Tyldesley, 35, played Rovers Return barmaid Eva Price on the ITV Soap from 2011-2018 and told This Morning on Thursday she was "so excited" and equally "terrified" because she "literally can't dance".
She said: "I love to dance on a night out if I've had a couple of drinks and me and Alfie [her son] silly dance in the kitchen but that's it, I'm terrified."
Teenage social media star Saffron Barker - whose book Saffron Barker Vs Real Life topped the Sunday Times bestseller list - said she was "very grateful for the opportunity", after she was announced as the fourth contestant.
Speaking to former Pussycat Doll and 2018 finalist Ashley Roberts on Heart Radio, Barker said: "I'm actually most excited to find out my partner, although I know I've still got to wait another month to find out."
She added that she was inspired by the success of another of last year's finalists, fellow YouTuber Joe Sugg. "I'm excited to follow in his footsteps," she declared. "He did absolutely amazing... I've got a lot to live up to."
EastEnders actress Emma Barton, who plays Honey Mitchell, was one of the first names to be announced in a reveal on The One Show featuring last year's winner Stacey Dooley.
Barton said she was a big fan of Strictly and was therefore "over the moon" to be asked to appear in series 17.
Image copyrightPA MEDIA
Former England goalkeeper David James said he was persuaded to compete by ex-contestant and former swimmer Mark Foster, who had an "amazing experience" on the dancefloor.
James, 49, who was the oldest player at the 2010 World Cup in South Africa, said he was "really excited" to be chosen and had "some big shoes to fill" following previous appearances by sports stars.
Comedian Chris Ramsey, who starred as Jack Pearson in the BBC Two sitcom Hebburn, said he was "really buzzing" but noted that while he is hungry for success, he has never been a natural shoe shuffler.
"You will not find me on the dancefloor at parties," said the 32-year-old. "You will find me at the buffet table... All night.
"At my wedding, I danced with my wife; that one song took about six months' practice, and I definitely stood on her feet a couple of times."
This year's series will see the return of judges Shirley Ballas, Craig Revel Horwood and Bruno Tonioli, but Dame Darcey Bussell will be replaced by Motsi Mabuse - sister of Strictly professional Oti.
Latin dancer Nancy Xu, a dancer in West End show Burn the Floor and a finalist on So You Think You Can Dance? in China, will replace the outgoing Pasha Kovalev as a professional dancer.
The final celebrity dancers in this year's line-up will be announced on Wednesday.