Although they have yet to officially confirm the baby's gender or name, reports surfaced that the couple had a baby girl and named her Violet.
“No that’s not the name," Reynolds clarified to USA Today. "I don’t want to get into that but I don’t know where that came from."
Reynolds, 38, and Lively, 27, announced last October that they were expecting by posting a photo of her baby bump to her website, Preserve.
Now that the baby has arrived, Reynolds said that fatherhood is all he can think about these days.
"It’s still so new that it’s hard to conceive being away for more than seven hours at a time. I had to go to Sundance this last week. I was more excited to get a good night’s sleep. It was borderline pornographic for me," he joked. "I don’t sleep very much. It’s great. It’s wonderful."