Rainier will be buried next to his wife, Hollywood star Grace Kelly, who died after a car crash in 1982, the BBC reported. Prince Albert, 47, one of the couple's three children, is succeeding him as the principality's monarch.
Ten soldiers from the Prince's Company of Carabineers carried his coffin out of the palace, crossing a square filled with thousand of people, many holding red and white roses.
Flags lining the streets, also tied with black ribbons of mourning, were at half staff, as Monaco observes an official three-month mourning period.
The prince died April 6 after a long illness.