A rep for Hudson confirmed yesterday that the actress had given birth to a "healthy baby boy" in LA.
Hudson updated friends on the 7 lbs, 12 oz child's condition in an email and urged them to donate to tree-planting organisation Barcham rather than purchase formal gifts, a source told US Weekly.
The star also encouraged loved ones to donate to Barcham for her June baby shower, which Courteney Cox and Rachel Zoe attended.
Bellamy and Hudson have yet to reveal their newborn son's name.
Hudson is also the mother to 7-year-old son Ryder Russell, who she had while married to Black Crowes frontman Chris Robinson. Robinson and Hudson divorced in 2007.
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Watch Kate Hudson in the trailer for Something Borrowed below: