The 'What I Like About You' actress revealed the news to her co-star Jennie Garth, as the pair recalled bumping into one another at an airport.
Speaking on the 'I Choose Me with Jennie Garth' podcast, the 'American Horror Story' star said: "It was so fun to get to run into you. And you also look so beautiful coming off this flight. "I was like, that's annoying. 'Why do you look so fresh?' "
Jennie said the reason for her look was because she wearing a "big hat", and then added: "Wait. You dropped a bomb on me right there in the airport baggage claim. "And you told me ... can I say?"
Leslie replied: "You know what's funny is I actually have not spoken about it yet, but you can say. "I don't want to ruin your moment." But Leslie continued: "I am engaged, which is so fun."
The 52-year-old star hasn't publicly revealed her fiancé's identity, and admitted she wasn't prepared for him to pop the question.
She said: "That's a wild thing that I didn't see coming. Not that I didn't see it coming with this person. "I just didn't see any of this next chapter of my life coming.
"He's a wonderful person. And it's so funny that this is the first time I'm talking about it publicly, Jennie.
"And it's so funny because I've known you for many, many years. You know me and my earlier iterations.
"So the fact that, you know, we get to see each other how we are now. I mean, it's a trip to be the age that I am. "It is a very lucky and wonderful next chapter.
"But, I mean, look. My whole life got reorganised around my 50th birthday, and everything got thrown up into the air, and it sort of fell to the ground.
"And I was very intentional about deciding what I was gonna pick up and what doesn't come with me anymore."
Leslie was previously married to Jon Bronson - who she has an adopted daughter, Goldie, 17, with - for 20 years, until he filed for divorce in April 2020.