President Juan Manuel Santos signed the agreement with the head of the ICC, Judge Sang-Hyun Song, who is in Colombia the scene of armed conflict for nearly a half-century on a two-day visit.
"Colombia is the first country in the Americas to enter into this agreement.
It is my hope that this will encourage other states in the region to follow its example," Santos said.
Colombia has seen decades of fighting involving the leftist Revolutionary Armed Forces of Colombia (FARC) Latin America's longest-fighting insurgency as well as right-wing paramilitaries and powerful drug cartels.
After signing the agreement with Santos, Song received a report from the local representative of the UN High Commissioner for Human Rights detailing alleged war crimes and crimes against humanity committed by armed groups.
The representative's office said the report gave special attention to the recruitment of and violence against children and adolescents, and also dealt with alleged extrajudicial killings by Colombian security forces.
Agreements like the one reached on Monday, which provide the legal framework for the possible enforcement of future sentences, have been signed by Austria, Britain, Belgium, Denmark, Finland and Serbia, the ICC said.