The Christmas-themed photos show the royal parents with their hands full with Princess Gabriella in pink and Prince Jacques in baby blue.
Gabriella was born first at 5.04pm, and Jacques at 5.06pm, but it is Jacques who will be the future Prince of Monaco, because of the Mediterranean principality's male inheritance laws.
They are the first children for the 36-year-old former South African Olympic swimmer, who married Prince Albert II, 56, three years ago.
Prince Albert was by his wife's side as the children were delivered by Caesarean on December 10 at the Princess Grace Hospital, which is named after Albert's mother, the late Hollywood star, Grace Kelly.
Soon after 7.30pm, 42 cannon shots rung around Monaco, confirming that the babies had been born.
The babies are the first twins in the royal household, which dates back to the 13th Century.
Albert said he didn't know the sex of the children before birth.
He said: "It is one of the beautiful surprises that life offers us."
Albert, the son of the late American actress Princess Grace, had worried some of his subjects with his long bachelorhood and his lack of a legitimate heir.
He married Charlene Wittstock, a Zimbabwe-born, South Africa-raised former Olympic swimmer in 2011. Her pregnancy was revealed in October.
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