"We feel so lucky to have been able to experience the miracle of birth once again and are forever grateful for the opportunity to be the parents of another little angel," the statement reads. "Vivian Lake was born at home on Dec. 5. She is healthy and full of life. Thank you all for your support and well wishes."
Vivian is the couple's second child together and first daughter. She joins older brother Benjamin Rein, who turns 3 on Saturday, as well as 5-year-old John, Brady's son from a previous relationship with actress Bridget Moynahan.
Brady, 35, and Bundchen, 32, have been married for three years.