Thousands of UN troops who have patrolled the zone will be phased out gradually and replaced by troops from a joint Ivorian army made up of former rebels and government troops.
On Monday, Soro and Gbagbo are to officially dismantle a checkpoint at Tiebissou, 42km from the administrative capital, Yamoussoukro.
"The country is being reunited, the war is over, dear friends and compatriots, the war is over," Ggabgo said at an army parade in Yamoussoukro.
After that they will move to a village inside the buffer zone for the beginning of the first joint patrol comprising an equal number of government and rebel forces, assisted by four UN police officers.
Fernand Amoussou, the UN forces commander, said in the run up to the exercise: "The process will be staggered over several weeks ... and will depend on the ability of the Ivorians" to take over from the international force.
The UN says it will remain on standby to combat any outbreak of violence in the clearance of the zone.
Observers fear the western region bordering Liberia, through which the buffer zone cuts, could pose the greatest threat to the smooth running of the exercise.
Amoussou said dismantling the zone will be "heavy and complex", admitting that the west of the country could be problematic.
The latest UN human rights report said rights conditions in the west of Ivory Coast "remained very alarming".
The end of the demilitarised zone will ease movement of people and goods between north and south.
It will also hasten the return of the government institutions to the north, deserted by civil servants in 2002 fleeing the fighting.
The UN's role has been relegated to that of an observer after the two protagonists signed a landmark deal which saw the ex-rebel chief appointed prime minister, and a new government installed within weeks of signing it.
On Friday, Soro asked for forgiveness "for all and in the name of all" and called for reconciliation during his first address to the nation.
In his own gesture towards reconciliation, Gbagbo has enacted a new amnesty law for national security crimes committed during the past six and a half years.
Ivory Coast's latest conflict started in 2002 with a rebellion, mounted by discontented soldiers from the mainly Muslim north who complained of being marginalised by the Christian-dominated government of Gbagbo.
Several mediation attempts by France, the former colonial ruler of the country, the UN and a west African regional bloc failed before the so-called homegrown deal signed on March 4.