The superstar couple welcomed Lucy and Nicholas on Dec. 16 in Miami. Iglesias, 42, and Kournikova, 36, began dating in 2001. The couple have kept the details of their relationship private and did not mention a pregnancy before the birth was reported by TMZ.
Mom and dad made separate Instagram posts Tuesday, with the same caption: "My Sunshine."
Kournikova retired from the WTA Tour in 2007. The Russian never won a Grand Slam and owned a 209-129 singles record. Kournikova won more than $3.5 million in prize money during her career.
Iglesias released his new song El Baño last week.