Baby on the Way for Seth Meyers

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There’s a bun in the oven!

Late Night host Seth Meyers and wife Alexi Ashe are expecting their first child, PEOPLE can confirm.

The couple made the announcement during the Natural History Museum Gala at the Museum of Natural History — whose board members include Late Night producer Lorne Michaels. Meyers’ MC’ed Thursday night’s event in New York.

“The couple was sharing the exciting news with friends and cast members at the event,” a source tells PEOPLE. “Everyone was coming up and congratulating the couple and giving them hugs. Seth and Alexi were beaming about the news of their baby!”

Meyers, 41, and Ashe, 32, tied the knot with an intimate ceremony in Martha’s Vineyard back in 2013, just a month after announcing their engagement.

Though small, their nuptials were a star-studded event, featuring the likes of Andy Samberg, Ali Larter, Olivia Munn, Jason Sudeikis and Amy Poehler, among others.

— Naja Rayne