"I don't have any picks, so we haven't really chosen one yet," Brady, 32, said Wednesday of their new arrival. "But everyone is great. Everyone is doing really well."
Bündchen, 29, delivered a baby boy Tuesday night, with her twin sister Patricia and mother Vania by her side for support.
"Gisele is absolutely thrilled. Why shouldn't she be?" says a source close to the supermodel. "She has a beautiful healthy boy!"
"She wants a big family like the one she came from and now is her time," says the source. "That's what she's always wanted most."
Brady, who also has a son Jack, 2, with ex Bridget Moynahan, is excited as well. "It's a wonderful experience in my life," he said.
With reporting by PETER MIKELBANK