A more elaborate religious ceremony to be attended by dignitaries from around the world is planned for Saturday.
Albert is the 53-year-old son of the late Prince Rainier and late film star Grace Kelly.
People.com said thousands of well-wishers cheered as video of the prince and his 33-year-old bride exchanging vows in the throne room was shown on screens outside the palace.
The new princess wore a pale blue suit and diamond earrings and the prince was in a dark suit for the occasion, People.com reported.
Reports that said Wittstock wanted to call of the wedding were rampant this week but palace officials vehemently denied there was any discord between the couple, who began dating in 2005.
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