The actor, 44, posted a black-and-white photo to Instagram of his baby's hand wrapped around his and Meyer's fingers.
"With full and grateful hearts we welcome our beautiful son into this incredible world," Galecki said. "Thank you for all of your love and support."
Meyer, a 22-year-old model, also posted a photo.
"With full and grateful hears we welcome our son into this world," she similarly captioned the photo. "Thank you for all your love and support."
Meyer announced back in October on Instagram that the baby would be named Avery.
"My amazing mama and auntie put together the most amazing celestial shower," she wrote on Instagram. "I am so grateful for the sweetest, most amazing night, celebrating Avery."