The 59-year-old was congratulated on the news by her BBC Breakfast colleagues Sally Nugent and Jon Kay as she reported from the Chelsea Flower Show.
The BBC weather presenter, who has not publicly revealed the name of her new fiance, told viewers she had become engaged on holiday.
Nugent told Kirkwood: “I’m a little bit concerned about you this morning. I don’t know how you’re managing to stand up with that giant rock on your left hand, Carol.”
The former Napier student replied, saying: “Oh that one, thank you Sal. It is rather nice, I got engaged.”
Nugent added: “Congratulations from all of us, it’s the happiest news, we are so so delighted, congratulations. Can we confirm to the nation what’s happened?”
Former Strictly contestant Kirkwood quipped: “Oh thank you, yes, I think you just have Sal! Yes, I got engaged, we got engaged when we were on holiday, so it’s lovely news and we’re both thrilled. So, thank you!”
The Scottish presenter was a contestant in the 2015 series of BBC One’s Strictly Come Dancing and was partnered with Pasha Kovalev.
She has never publicly named her long-term partner, who has been described previously in reports as her “secret boyfriend”.
Last year she published her debut romantic novel titled Under A Greek Moon, about a Hollywood actress embroiled in a scandal who returns to the Greek island where she fell in love with an enigmatic tycoon.
Speaking while promoting the book, she told the PA News agency of her partner: “He’s only a secret boyfriend because I never talk about him.
“I always feel that through my job, I put myself in the public eye and am very happy, but my partner and my family and my friends haven’t, so I’m hugely respectful of their privacy.
“I just don’t talk about them, other than to say that my partner is drop-dead gorgeous, he’s funny, he makes me very happy.”
She added: “He gets up at quarter to three in the morning to make me a cup of tea before going to work – if that’s not romantic, I don’t know what is.”
A host of people congratulated Kirkwood on the happy news, among them BBC Breakfast sports presenter Mike Bushell, who tweeted: “Wow wow what fabulous news to wake up to today. Huge congratulations to wonderful friend and colleague @carolkirkwood – so chuffed for you on your engagement”.
Former BBC Breakfast presenter Dan Walker tweeted: “Carol Kirkwood is the best of us. Delighted she has found someone who can handle her headlock hugs. Congratulations Carol. If you get married live on #BBCBreakfast can I come back for a one off?”
She was previously married for 25 years to businessman Jimmy Kirkwood before they divorced.