The boy is Kate's first child with Muse frontman Matt Bellamy and the couple are said to be thrilled with their new arrival.
Kate, 32, recently revealed she couldn't wait to meet her unborn baby because she wanted to find out its sex.
She said: "I'm really excited. I'm not in a rush, I don't have nerves, I'm so excited to have another baby, for our family, we are all really happy, so I can't wait.
"And I'm getting to the end, so I'm like, 'Ahhh, what is it going to be, who is it, is it going to come out screaming, is it going to come out quiet, is it going to have eyes open, is it going to be shut, is it going to have hair?'"
Earlier in her pregnancy, Kate revealed that her son thinks she is going to have a girl.
She said: "It feels like a girl, but I don't know. Ryder thinks it's a girl."
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