“I kept saying, ‘Stop joking around. Stop joking around,” she continued. “But it was so great.”
Cohen also complimented Michele on the four-carat diamond ring Reich personally designed for his bride-to-be with Leor Yerushalmi and The Jewelers of Las Vegas.
“Someone had tweeted in wanting to know if you need a crane to carry your ring,” he joked. “It’s gorgeous.”
“I keep thinking it’s borrowed and I have to give it back at some point,” Michele said.
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A source close to the pair told PEOPLE “the couple couldn’t be happier” with their engagement.
“It was so romantic and she’s just so excited and feels so lucky. He’s a really nice guy,” the insider added.
RELATED VIDEO: Lea Michele Is Engaged!
The pair dated for over a year before Reich, the president of clothing company AYR, proposed.
Sharing the happy news alongside a photo of her gorgeous engagement ring, Michele simply captioned the snap, “Yes.”
Michele previously told PEOPLE that Reich helps her stay grounded.
“When I’m not working, I’m at home with my cat, with my family, with my boyfriend, with the people that I love — and that’s how I reset, and that’s how I center myself,” she said. “It’s so important to tune out the noise and the unnecessary, and just focus on the people that you love, because they know you better than anyone.”
She added: “I’m very happy and I think that you can tell. I don’t really talk a lot about my personal life, but I’m also the kind of person where I always say, ‘You will see how happy I am just by looking at my face.’ I can’t hide it.”