"Everyone here is extremely, extremely happy," the palace said.
No wedding date has been for the prince, 52, and the former schoolteacher, 32. The couple first appeared in public together at the 2006 Winter Olympic opening ceremonies in Turin, and Wittstock has been living in Monaco since 2007, when she unofficially ended her training.
She has become friends with and been tutored in protocol by both his sisters, Princesses Stephanie and Caroline. "But she knows instinctively what is expected of her," a royals source tells PEOPLE.
Last weekend, Albert and Wittstock were in Stockholm to attend the wedding of Crown Princess Victoria of Sweden and Prince Daniel Westling, Duke of Vastergotland.
This will be a first marriage for Monaco's monarch, who is the son of the late film star Grace Kelly and the late Rainer III, Prince of Monaco.
In 2005, Albert officially acknowledged a toddler son he'd fathered with a Togolese flight attendant. The following year, he also acknowledged a second child born out of wedlock: a daughter, now 18, in California.