The “El Baño” singer snuggled up to his baby — who was wearing a gray striped onesie and matching hat in the sweet photo — and wrote, “My Sunshine.”
In a separate post to her own social media account, Kournikova copied Iglesias’ caption as she smooched the cheek of the other baby, who was also wearing a gray onesie.
Iglesias, 42, and Kournikova, 36, reportedly welcomed the twins — a boy and a girl — in December, according to TMZ. The outlet said that the babies’ names are Nicholas and Lucy, and that they were born in Miami.
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A rep for the musician had no comment, while a rep for the athlete did not immediately return PEOPLE’s request for comment at the time. A source confirmed to PEOPLE that Kournikova was indeed pregnant.
The newborn babies are the first children for the couple, who have been together for over a decade and a half.
A source told PEOPLE late last year that they saw Kournikova’s “cute belly,” adding, “a friend told me like five months ago [that] they were pregnant, but keeping it very, very undercover.”
The insider continued, saying the couple was “very private but very generous with local charities.”
Iglesias has long thought Kournikova would be the “ideal mother,” telling PEOPLE en Español in 2007, “I think she’d be the perfect mother, and I say it regardless of whether I’d be with her or not.”