Bouchard, who broke up with NFL player Mason Rudolph last year, took to social media on Thursday, September 28, to share footage her embracing Brinkley-Cook on a waterfront terrace.
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"Baby boy," Bouchard wrote on Instagram.
Several fans reacted to the official news, with Stephens among those sending in their thoughts and congratulations.
"Cuties!!!!!! ❤️❤️❤️" commented Stephens on the photo.
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Jack Brinkley-Cook is the son of the renowned supermodel Christie Brinkley. Although the couple have been seen together since summer of last year, they kept their relationship private until now.