Gabriella and Jacques' appearance will come almost a month after they were welcomed into the world on 10 December.
The couple will present their son and daughter on 7 January
In the two days since the birth there has been an outpouring of well wishes from royal fans who have been leaving flowers and signing an online guestbook in celebration.
Prince Albert and his Zimbabwe-born wife Charlene have requested that instead of sending gifts, supporters should make donations to the charities and organisations promoted by the couple.
On Thursday Prince Albert thanked the people for their good wishes in a video message for his "dear countrymen and inhabitants of the principality".
Framed notices announcing Gabriella and Jacques' birth were placed on the palace
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.
"Thank you to all those in Monaco and around the world who have expressed their attachment to the princess, myself and my family," he said. "We thank God for this great happiness."
According to Monaco's inheritance law, which favour males, Jacques is his father's heir and will be known as His Serene Highness The Hereditary Prince of Monaco, Marquis of Baux.
Gabriella takes the title of Her Serene Highness The Countess of Carladès.