The actressโ 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.
โThe baby is extremely healthy and is surrounded by friends and family in L.A. Anne and Adam are ecstatic to be parents,โ a pal told the website.
Anne, 33, has never shied away from the fact sheโd love to start a family.
โOh, my God. I want to be a mother, and I anticipate loving my children quite fiercely,โ she explained to Vogue in 2013.
โI think about it all the time, though itโs a silly thing to think about because the kind of mother Iโll be depends on the kind of children I have. I canโt wait to meet them,โ 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.
โโI 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 canโt help it,โ the Interstellar star told Harperโs 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.

Anne confirmed her pregnancy in January by sharing this sweet snap on Instagram.
Meanwhile, it looks like this is just the beginning of one big happy family.
Anne previously told the UKโs Telegraph sheโd love a large brood.
โIโm 30 and I want to have a family of a certain size. Look, Iโll start with one healthy kid but Iโd like to have a few naturally and adopt. I gotta get on it, you know? Iโd 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,โ she said at the time.
Congratulations to Anne and Adam on the safe arrival of Jonathan!

This is the first child for Anne and Adam, who married in 2012.