The actress' rep confirmed the exciting news to US Weekly.
According to E! News, the pair welcomed their first child together in LA on March 24 and have named him Jonathan Rosebanks Shulman.
"The baby is extremely healthy and is surrounded by friends and family in L.A. Anne and Adam are ecstatic to be parents," a pal told the website.
Anne, 33, has never shied away from the fact she'd love to start a family.
"Oh, my God. I want to be a mother, and I anticipate loving my children quite fiercely," she explained to Vogue in 2013.
"I think about it all the time, though it's a silly thing to think about because the kind of mother I'll be depends on the kind of children I have. I can't wait to meet them," she added.
Watch the wonderful way Anne confirmed her pregnancy in the player below. Post continues after the video!
Anne married fellow actor Adam, 35, in 2012 in a stunning ceremony in Big Sur, California.
"'I knew from the second I met him that he was the love of my life. He walks into a room, and I light up. I can't help it," the Interstellar star told Harper's Bazaar of her man.
The Oscar winner officially confirmed her pregnancy in January this year by uploading a beach-side photo of herself in a bikini, proudly showing off her beautiful bump.
Meanwhile, it looks like this is just the beginning of one big happy family.
Anne previously told the UK's Telegraph she'd love a large brood.
"I’m 30 and I want to have a family of a certain size. Look, I’ll start with one healthy kid but I’d like to have a few naturally and adopt. I gotta get on it, you know? I’d like to have as many as I can afford, not just financially but in terms of time, because you want to make sure each one feels special," she said at the time.
Congratulations to Anne and Adam on the safe arrival of Jonathan!
- MindHow to mind your memory by giving your brain a regular workout
Australian Women's WeeklyYesterday 5:11pm
- British Royal FamilyTrial date has been set for the defamation case against Meghan Markle
Now To LoveYesterday 1:45pm