The rebels should have all their arms turned in by June, Santos said.
"This weekend the process of mobilisation toward the zones was completed and the protocols of the bilateral and definitive ceasefire and the abandonment of arms has begun," Santos said in southern Putumayo province.
The Revolutionary Armed Forces of Colombia (FARC) signed a peace agreement with the government in late 2016 to put an end Latin America's longest-running armed conflict, which killed more than 220,000 people.
FARC rebels have crisscrossed Colombia on foot and by boat from their jungle and mountain camps to 26 zones monitored by UN personnel.
Under the terms of the peace accord, the FARC, which began as a peasant uprising 52 years ago, will form a political movement in the South American nation.
The accord has been heavily criticised and was initially rejected in a referendum for being too lenient on the rebels, who will be spared jail time.