Here is his reaction in full:
He said: "I'm very excited to announce that Meghan and myself had a baby boy earlier this morning, a very healthy boy. Mother and baby are doing incredibly well. It's been the most amazing experience I could ever have possibly imagined.
"How any woman does what they do is beyond comprehension, but we're both absolutely thrilled and so grateful to all the love and support from everybody out there. It's been amazing, so we just wanted to share this with everybody."
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Asked if they had any names yet, he said: "Still thinking about names. The baby is a little bit overdue, so we've had a little bit of time to think about it.
"That's the next bit, but for us I think we will be seeing you guys in probably two days' time as planned as a family to be able to share it with you guys and so everyone can see the baby."
Asked what it was like to be present for the birth, he laughed and said: "I haven't been at many births. This is definitely my first birth. It was amazing, absolutely incredible, and, as I said, I'm so incredibly proud of my wife.
"As every father and parent will ever say, you know, your baby is absolutely amazing, but this little thing is absolutely to-die-for, so I'm just over the moon."