The couple welcomed a baby boy, who they have named Jonathan Rosebanks Shulman, on 24 March, Hathaway's representative confirmed to E! News.
"The baby is extremely healthy and is surrounded by friends and family in L.A.," a source added.
"Anne and Adam are ecstatic to be parents."
The 33-year-old actress confirmed her pregnancy in January 2016 after realising the paparazzi were trying to get photos of her bump.
She shared an Instagram photo of herself in a bikini.
"I figure if this kind of photo is going to be out in the world it should at least be an image that makes me happy (and be one that was taken with my consent. And with a filter," she wrote.
Hathway and Shulman began dating in 2008 and married in California in September 2012.
The new mother has been public about her desire to have a family in the past.
"Oh, my God. I want to be a mother, and I anticipate loving my children quite fiercely," she told 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."