Their parents, Prince Albert II and Princess Charlene of Monaco, presented them to a crowd of flag-waving onlookers from the balcony of the royal palace.
Each carrying a baby swaddled in white blankets, the proud couple smiled and waved as the crowd cheered and applauded, while church bells rang and a military band played.
The infant royals appeared to sleep through the event, for which a public holiday was declared.
The twins were born on December 10 at the Princess Grace Hospital in Monaco, a tiny principality bordered on three sides by France and on the fourth by the Mediterranean Sea.
Gabriella Therese Marie arrived in the world two minutes ahead of her brother. But in line with Monaco's rules of succession, Jacques Honore Rainier was named the Crown Prince and his sister next in line to the throne after him.
"A beautiful Christmas gift to Monaco, friends of the Principality of Monaco and the royal family," said the post.
One of the tiny additions to the royal family wears a pink babygrow and the other a blue one.
The twins are the first children born to Charlene Wittstock, a former South African Olympic swimmer who married Prince Albert II in 2011.
Prince Albert, 56, also has two children born out of wedlock in 1992 and 2003 who are not in line for the throne.
He succeeded his father, Prince Rainier III, as Sovereign Prince of Monaco on his death in 2005.
At 2.02 sq km (77 sq miles), it is the second smallest state in the world, after the Vatican, and about half the size of New York's Central Park.
It sits on the French Riviera and is a popular tourist destination, famous for its casino and luxury hotels.