The royal couple welcomed a little girl and a little boy, and have named their newborns Gabriella Thérèse Marie and Jacques Honoré Rainier.
A statement released from the Palace read: "It is with immense joy that TT.SS.HH the prince and princess of Monaco have the great pleasure to announce the birth of their children named: Gabriella, Thérèse, Marie (born at 17h04) Jacques, Honoré, Rainier (born at 17h06).
"The births took place on 10 December 2014 at the Maternity of the Princess Grace Hospital Monaco. The princess and the children are doing well."
The statement continues: "The Prince Jacques, Honoré, Rainier is the crown prince.
"In accordance with the historic custom established by the treaty of Péronne (1641), He shall receive the title of Marquis of Baux (in Provence).
"The Princess Gabriella, Thérèse, Marie, second child in the line of succession, shall receive the title of countess of Carladès (in Auvergne)."
Albert had previously cleared up the issue of succession, stating: "In the case that one is a girl and the other a boy, it will be the boy." The little boy will in due course become sovereign in his father's place, inheriting an estimated $1billion fortune along with the leadership of the Grimaldi clan, which has ruled Monaco since the 13th century.
In celebration of the new arrivals, churches in the tiny state rang their bells for 15 minutes, followed by boat horns. Meanwhile, at Fort Antoine, a fortification dating back to the 18th century, 21 cannon shots were fired for each child – just as they were for their father's birth 56 years ago.
A proclamation about the twins, signed by the prince, will also be displayed at the entrance to the palace in Monte Carlo.
A few days later the parents will present their children to their countrymen, just as Albert's own parents Prince Rainier and Princess Grace did.
While it is a day of national rejoicing, the birth of the babies three years after her high-profile wedding marks the fulfillment of a dream for Charlene. The 36-year-old former Olympic champion has previously spoken of how much she wanted to start a family – as well as hinting at the expectations placed on her.
"We had a big wedding. It was a big adjustment after that," the royal said in an interview with South African newspaper Sunday World.
"Now I'm settled and I think kids will come. I don't put any pressure on myself," she added. "If it happens, it happens."
Charlene's husband had chosen not to find out the sex of the twins beforehand, asking his wife not to let on. He told Monaco Matin newspaper: "The princess probably knows but she is playing the game. She is keeping the secret as I asked her to.
"You know, one doesn't often have the opportunity to have such pleasant surprises in life, that is why I prefer not to know the babies' gender before the birth."