The couple took their vows in a ceremony before several dozen guests in the palace's red silk-walled throne room, where Grace and Rainier also married.
"Oui," both responded in voices so soft as to be barely audible, when asked if they took each other as their spouse. The marriage became official - and Monaco finally had its princess - when the president of Monaco's Council of State, Philippe Narmino, who officiated the ceremony, pronounced, "I declare you united by the bonds of marriage."
Many of Monaco's 7,618 citizens braved the scorching sun to watch the ceremony live on two giant screens set up in front of the palace, some of them decked out for the occasion in suits or formal gowns and heels.
Cheers erupted from the crowd when, after the 15-minute-long ceremony, the newlyweds emerged from a window to wave at their subjects. The couple's brief, embarrassed peck on the mouth garnered even more enthusiastic applause.
Long regarded as one of Europe's most eligible bachelors and known for his string of romances with some of the world's most beautiful women, Albert, 53, long eschewed marriage. His reluctance to settle down was known to have exasperated his father and made many here despair of his ever tying the knot.
Albert acknowledged having fathered two children out of wedlock - a now-teenage daughter with a California woman and a little boy with a stewardess of Togolese origin.
Wittstock was born in Zimbabwe but moved to neighboring South Africa when she was 12, and under the tutelage of her mother, a swim coach, competed for that country at the Sydney Olympics in 2000. Like his wife, Albert is a former Olympic athlete. A member of the International Olympic Committee since 1985, he competed in five Winter Olympics as part of Monaco's bobsled team. Albert met Wittstock during a 2000 swimming competition in Monaco.
On Saturday, the religious wedding will take place in the Main Courtyard of the Prince's Palace. Wittstock, on her father's arm, will walk along a red carpet to the altar. The Archibishop of Monaco will celebrate the Mass. About 3,500 people are expected to attend the festivities.