"Oh, he just loves children," says Kay. "Can't you just see it? Matthew with his surfboard walking the beach and a gang of kids following him with their surfboards saying, "We're coming, Papa!"

Kay spoke to her son shortly after Levi arrived last night.

"Matthew is over the moon," she said in an exclusive interview just minutes ago. "And he is so proud of Camila. I think it's excellent that men are allowed in the room when women give birth. He loves Camila, but now he really sees how strong she is."

As for the baby's Bible-inspired name, Kay cooed, "It's so strong. Just say it: Levi McConaughey. That's no wimpy name."

Grandma McConaughey, whose grandchildren call her "MaMac," is flying from her Texas home to Los Angeles on Thursday to meet her newest grandchild. And she's already got a gift for the baby. "I'm giving him Matthew's baby book," said Kay, author of the inspirational self-help book I Amaze Myself. "You can't buy that. It's one of a kind."

She jokingly warns friends and family not to bother buying any clothes for Levi. "Just get him flip-flops and a bathing suit," she laughed. "You know that kid's not going to be wearing a lot of clothes."