As the tiny state celebrated, the proud father recorded a video message in French, for his "dear countrymen and inhabitants of the principality".
Twins Gabriella Thérèse Marie and Jacques Honoré Rainier were born on Wedensday afternoon
The 56-year-old sovereign begun by confirming that his "beloved wife" had given birth to two children called Gabriella Thérèse Marie who was delivered at 5.04pm, followed two minutes later by Jacques Honoré Rainier.
Albert went on to say: "Thank you to all those in Monaco and around the world who have expressed their attachment to the princess, myself and my family. We thank God for this great happiness."
The couple have largely gone with tradition, giving the babies names which have special meaning within the royal family. Their births were announced to great joy in Monaco, with church bells ringing and 21 cannon shots fired for each child.
Proclamation of the twins' birth placed outside the palace
Prince Albert's baby pictures
According to the principality's inheritance law which favour males Jacques is his father's heir. He will be known as His Serene Highness The Hereditary Prince of Monaco, Marquis of Baux.
He is named after Jacques I, who came from an ancient Norman family and reigned in the 18th century. Meanwhile, five Honorés have sat upon the throne of Monaco.
Rainier is, of course, to honour Albert's beloved father, who died almost ten years ago on 6 April, 2005.
Jacques' sister is Her Serence Highness The Countess of Carladès. Gabriella seems to have been a personal choice for the couple, perhaps picked by 36-year-old Charlene herself.
As for her other names, there was a Monegasque princess in the 18th century called Marie Thérèse de Choiseul, known for her beauty, mischievous behaviour and courage. Marie is also one of the middle names of Charlotte Casiraghi, Albert's niece.