O'Donnell told her Rosie Show viewers that she was reluctant to publicly announce her wedding plans, but had no choice because an audience member overheard her speaking to a guest about the engagement and posted the news online.
"Michelle said to me a few months ago, when we got engaged, she said, 'How come you didn't say it on your show?' And I was like, 'Honey, I don't know how'. I didn't know how to say it," O'Donnell said.
The Rosie Show host also quipped: "You don't want to become one of those celebrities that talks about their relationship ad nauseum and makes it into a fairy-tale thing… And then they go and have an affair with somebody. I don't want to say any names."
Rounds and O'Donnell reportedly first met while waiting in line at a Starbucks several months ago.
O'Donnell was previously married for three years to Kelli Carpenter and is the mother to four children.
The Rosie Show airs weeknights at 7/6c on the Oprah Winfrey Network.
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Watch Rosie O'Donnell discuss her engagement on The Rosie Show below: