Indigenous communities have suffered some of the worst violence One of the aims is to return land to up to four million people forced from their homes by rebels, paramilitaries and traffickers.
However, implementing the law will be a huge challenge and officials estimate it may take a decade to restore land.
For more than 40 years, Colombia has seen fighting and violence by guerrillas, paramilitaries and drug gangs, and the security forces.
This led to Colombia having one of the largest populations of internally displaced people, officially put at 3.4 million by the UN refugee agency, the UNHCR.
The conflict has lessened in recent years but the process of giving financial compensation to victims and returning land to people will be a huge logistical task.
Moves to restore land are already under way but illegal armed groups have tried to undermine the process.
Several local leaders who campaigned for their communities to return to their land have been killed in recent months, rights groups say.
The law stipulates that those who qualify for compensation are the victims of "armed conflict", thereby differentiating them from the victims of common crime.
Mr Santos's predecessor as president, Alvaro Uribe, fiercely resisted this wording, arguing that it equated the state's actions with those of the illegal armed groups.
As a result, the law does not describe the armed groups as belligerents but as "terrorists", with the armed forces able to pursue them in defence of Colombian society.
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