"The wedding will occur on Aug. 31," a spokesperson for Monaco's Pink Palace tells PEOPLE. "It will be a private ceremony."
The couple, who have dated for seven years and have a son, Sacha, born last March, were schoolmates together at Paris's Lycée Fontainebleau.
They were introduced by Casiraghi's sister Charlotte and have been engaged since July 2012.
Casiraghi, who is Caroline's eldest son, is second in line to succeed his uncle, Prince Albert II, as Monaco's ruling sovereign. Santo-Domingo is a Colombian heiress and fashion designer.