The 27-year-old beauty gave birth to the couple's first child on Tuesday evening in Monaco's Princess Grace Hospital.
Raphaël's birth was announced by the president of the National Council, Laurent Nouvion, at a late meeting of the High Assembly. "The royal family has a new member," he said.
Princess Charlene and Prince Albert of Monaco were the first visitors to congratulate Charlotte and see baby Raphaël in hospital, in the same maternity ward where Charlotte herself was born.
The royal family requested the "Suite Maternité" — a 70 square metre bedroom with a bathroom, living area and state-of-the-art technology — for Charlotte.
French comedian Gad, who has a 12-year-old son named Noé from his previous relationship with actress Anne Brochet, has no doubts that his girlfriend will be an excellent mother.
"Charlotte is very intelligent and has a great sense of humour," Gad told PEOPLE. "She's doing well and is so excited about becoming a mother.
"She will be the best mother in the world because she's generous and loving. She has all the right qualities to be a good mother.
Gad, 42, also spoke about the first time he met Charlotte in 2011.
"We don't have a crazy love story, nor a fairytale," he admitted. "The most beautiful stories are the ones that are real. The great thing is that we were friends before.
"When you know someone first as a friend, you get to know them and you talk a lot, and then you really understand who the other person is."
The actor has been lovingly welcomed by Charlotte's family and it seems that the royal's mother, Princess Caroline of Monaco, has developed a soft spot for her daughter's boyfriend and loves to laugh at his jokes.
The couple has previously denied rumours that they are engaged, with Gad saying that "maybe one day" it would happen.