The palace issued a statement announcing the engagement of "His Serene Highness" and Ms Wittstock, who worked as a teacher before moving to the Mediterranean principality.
The palace did not indicate a planned wedding date, but the statement puts to rest months of speculation that the two long-time companions would wed.
It will be the first marriage of a reigning prince since Hollywood star Grace Kelly married Albert's father, Prince Rainier III, in 1956. She died in a car accident in 1982, casting a pall of tragedy over the dynasty.
Palace spokeswoman Laetitia Pierrat said Albert, 52, met South African Ms Wittstock, 32, in 2000 when she was in Monaco for a swimming competition. She has lived there since 2006. Asked if Ms Wittstock was pregnant, Ms Pierrat said: "I don't think so."
Ms Pierrat said royal couples had to wait at least six months between the announcement of the engagement and the wedding day.
Colombe Pringle, executive editor of French celeb magazine Point de Vue commented: "He's 50-something. It's time."