The actress, 32, gave birth to a baby boy.
Leading up to the delivery, Hudson told reporters she did not know the sex of her unborn baby – but suspected it would be a girl.
The couple’s first child together was born in Los Angeles.
Hudson has a seven-year-old son, called Ryder, with rocker ex Chris Robinson. The newborn is Muse frontman Bellamy’s first child.
The couple became engaged in April (11).