"I want to share with you the most important and moving moment of my life: the birth of my son," said Casillas, captain of Spain's World Cup and double-Euro-winning national team.
Martin, who weighed 3.85 kilos (8.5 pounds), and his mother "are perfectly well and are now resting", he added, in a statement sent to fans.
Casillas, 32, won the hearts of Spaniards when he kissed Carbonero, 29, live on air as she interviewed him after Spain's victory over the Netherlands in the 2010 World Cup final.
The couple have been together for more than four years now.
And so Casillas starts 2014 with a bang after having problems on and off the pitch in 2013.
He lost his first-team spot to fellow keeper Diego López under former Real Madrid manager Jose Mourinho, a trend which has continued under current coach Carlo Ancelotti.
He has also suffered injuries to his hand and rib cage.
On a more personal note, 2013 was also the year in which Casillas was embroiled in a feud with his parents over the running of his asset management firm, having decided to remove them as the main administrators.
Casillas posted the following photo of himself and his son Martín on his website on Monday.