The future king thanked journalists who waited hours on the clinic's steps in the rain before announcing the Caesarean birth of his daughter, Leonor, Hellomagazine.com reported.
"It's the most beautiful thing that can happen to anyone in life," he said. "Seeing your child being born is just amazing. We are radiantly happy."
Leonor, born three weeks early, "seems strong" and his wife is doing well, he added.
The new princess is second in line to the throne, but unless current law is changed, she would have to cede her position if her parents have a son.