The baby was born Dec. 8. But the day after the birth, Brady said he and Bundchen hadn't chosen a name. Word finally came out Friday when Bundchen posted a holiday message on her Web site.
Bundchen revealed the baby's name when she wrote, "Benjamin is a blessing and I could not be happier."
Brady and Bundchen were married in February. Benjamin is Bundchen's first child. Brady also has a 2-year-old son, Jack, with actress Bridget Moynahan.
Brady had joked earlier in the week about how hard it was to sleep with a new baby in the house, saying it was "a little tough early." He added, "It's coming."