The celebrity couple welcomed Lucy and Nicholas in Miami on Saturday, TMZ reported.
Kournikova, 36, and Iglesias, 42, have been dating since 2001 when they met on the set of Iglesias' "Escape" music video and have been known to keep details of their relationship private.
Iglesias has often avoided questions regarding rumors about the couple's marriage stating he doesn't believe the couple needs a "piece of paper" to affirm their love.
When asked in 2016 about plans for him and Kournikova to marry, Iglesias hinted a wedding may have already occurred.
"Who knows what the future holds ... or the past," he told E! News.
Both Iglesias and Kournikova shared photos of themselves on a boat in Miami on Saturday and neither mentioned the birth.