He said the "great paradox" of peacemaking was that "the victims are the ones who are most willing to forgive, to reconcile and to face the future with a heart free of hate".
In a deviation from his prepared remarks, he asked the representatives of the victims present to stand and be recognised for their own efforts in the peace process, to much applause.
He has previously pledged to donate the prize money - eight million Swedish krona ($925,000) - to help the conflict's victims.
"I have served as a leader in times of war - to defend the freedom and the rights of the Colombian people - and I have served as a leader in times of making peace," he said. "Allow me to tell you, from my own experience, that it is much harder to make peace than to wage war."
No war on drugs
Mr Santos said it was "time to change our strategy" on drugs, and that Colombia had "paid the highest cost in deaths and sacrifices" in the so-called war on drugs.
Media captionColombian President Juan Manuel Santos speaks to HARDtalk’s Stephen Sackur
The term, coined by US President Richard Nixon more than four decades ago, refers to US-led efforts to stop drug production at its source. In Latin America this has included on-the-ground policing, and fumigation of coca fields from the air.
"We have moral authority to state that, after decades of fighting against drug trafficking, the world has still been unable to control this scourge that fuels violence and corruption throughout our global community," he said.
"It makes no sense to imprison a peasant who grows marijuana, when nowadays, for example, its cultivation and use are legal in eight states of the United States.
"The manner in which this war against drugs is being waged is equally or perhaps even more harmful than all the wars the world is fighting today, combined."
Other laureates
Nobel prizes in the sciences, economics and literature were awarded at a separate ceremony in Stockholm.
Bob Dylan, the first songwriter ever to receive the prize for literature, was the only one who did not collect in person, having said in advance that he was unable to attend due to previous commitments.
He received a standing ovation nevertheless, and the Nobel Committee praised the poetry of his song-writing as "worthy of a place beside the Romantic visionaries".
Media captionPatti Smith restarted her performance half way through, telling the audience: "I'm sorry, I'm so nervous"
The singer-songwriter Patti Smith performed his song A Hard Rain's A-Gonna Fall, but forgot the lyrics part way through and apologised to the audience, saying she was nervous.
The other Nobel prizes given out by the Swedish King Carl XVI Gustaf were:
Physics: David Thouless, Duncan Haldane and Michael Kosterlitz
Chemistry: Jean-Pierre Sauvage, Fraser Stoddart and Bernard Feringa
Medicine: Yoshinori Ohsumi
Economics: Oliver Hart and Bengt Holmstrom
Image copyrightGETTY IMAGESImage captionMr Santos (left) and Farc leader Timochenko (right) signed the original agreement in June
The Colombian government's peace deal with the Farc was struck after many years of negotiations.
It hit a surprise hurdle in October this year when 50.2% of voters rejected it in a referendum.
Just four days after the unexpected referendum result, it was announced that Mr Santos would receive the prize. In his speech, he said the nomination was "equally surprising" and "came as if it were a gift from heaven".
Working alongside the no campaigners, the government wrote a new deal which was approved by Congress last month.
There were many armed groups involved in decades of conflict in Colombia, including left-wing rebel groups and right-wing paramilitaries. In October the government announced it would start peace talks with the second-largest rebel group, the ELN.