The singer and athlete welcomed twins — a boy and a girl — on Saturday in Miami, Florida, TMZ reports. Their names are reportedly Nicholas and Lucy, according to the outlet.
“I saw her cute belly,” a source tells PEOPLE. “A friend told me like five months ago [that] they were pregnant but keeping it very, very undercover.”
The source continued, saying the couple was “very private but very generous with local charities.”
“They basically only hang out with family and very close friends,” the source says. “They mostly keep to themselves.”
The newborn babies are the first children of both Iglesias, 42, and Kournikova, 36, who have been together for over a decade.
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“I absolutely want to have children, whether I have my own or adopt,” said the Russian retired tennis star, adding, “I love taking care of people.”
Continued Kournikova, “[Marriage] isn’t important to me. I’m in a happy relationship — that’s all that matters … I believe in commitment. I believe in being open and trusting each other and respecting each other completely.”
Iglesias told PEOPLE en Español in 2007, “The only thing I can say is that, in my opinion, Anna, whether we are together or not, would be an ideal mother.”
“I think she’d be the perfect mother, and I say it regardless of whether I’d be with her or not,” added Iglesias of the former The Biggest Loser trainer.