The couple, who began dating in 2012, were pictured leaving St Mary’s Hospital in London on Monday, with The Faculty actor pictured carrying a baby basket as they left the premises.
Meanwhile St Trinians’ star Tamsin still managed to look effortlessly beautiful in the days after the birth, stepping out in a simple autumnal outfit with her blonde hair pulled back off her face.
Neither party have confirmed whether they’ve welcomed a boy or girl this winter.
Josh, 37, and Tamsin, 27, are thought to have met on the set of The Lovers in 2010, though they didn’t become an item until two years later - when they faced each other in film Singularity.
Hartnett was previously linked to Scarlett Johansson, Amanda Seyfriend and Mischa Barton - though has been extremely private about his relationship with Tamsin.
And the Brit actress seems to have the same approach, sharing very little about her relationship with the Hollywood hunk on her social media channels.