The couple, who have been dating on and off since 2001, reportedly welcomed their newborns on December 16.
The twins, Lucy and Nicholas, are the first children for both the Iglesias, 42 and Kournikova, 36.
While the couple don’t often open up about one another, Kournikova told Women’s Health in 2011 that kids were definitely on her agenda, but marriage wasn’t a priority.
'I absolutely want to have children, whether I have them on my own or adopt,' she revealed.
The couple, who are notoriously private, are rarely photographed together.
Congratulations to the new parents!