Sam wrote: "Yesterday on the birthday of my Mum we welcomed Charlie Lane Wood. There were tears, Snezana you are my everything and my love and admiration for you somehow only grows stronger. The last 30 hours have been magical."
While Snezana added: "Another beautiful little girl to drive Daddy crazy. Charlie Lane Wood you are a little drop from heaven."
The pair share one-year-old daughter Willow and 14-year-old daughter, Eve, from Snez’s previous relationship.
Sam and Snez announced they were expecting just months after they tied the knot in a magical Byron Bay wedding.
He told Who exclusively in February: "Snez fell pregnant just a couple of weeks after the wedding ... it was a honeymoon baby!"
Speaking about how she broke the news, Sam said: "She walked into the room with a pregnancy test and started laughing at me, and I just knew!"