This is the first child for the Oscar-winning actress and her fiancé Darren Aronofsky

Oscar winner Rachel Weisz has had a boy, the star’s rep tells PEOPLE exclusively.

Mother, father (Darren Aronofsky), and child are healthy and happy, according to the rep.

Weisz, 35, is engaged to Brooklyn-born Requiem For a Dream director Aronofsky, 37. This is the first child for the couple, who are based in New York.

When she first revealed the pregnancy in January on the Tonight Show, the Cambridge-educated actress said of Aronofsky, “I found myself a sophisticated, educated American. He’s not an actor. He’s traveled the world. He knows where Europe is, unlike a lot of Americans. He’s very cultured, but he’s all man.”

Weisz won an Oscar in March for her supporting role as a political activist in The Constant Gardener. She also starred in both The Mummy and The Mummy Returns.

Next up, she’ll star in The Fountain, a sci-fi love story directed by Aronofsky.

Of Weisz’s pregnancy cravings, Aronofsky told PEOPLE last month, “I was expecting all the weird things. There’s this jar of pickles sitting in the fridge. It’s been there for months and she hasn’t even eaten one.”

As for the baby’s name, Weisz said backstage at the Oscars that she and her fiancé had narrowed it down to “a few” choices, adding, “Oscar isn’t amongst them, for sure.”