The National Liberation Army, or ELN - the South American country's last active rebel group - welcomed the decision in a statement.
"These elections are very special: it is the first time in half a century that the FARC, instead of sabotaging the elections, is participating in the elections".
"For many people it is hard to swallow Farc leaders campaigning on the streets", said Kristian Herbolzheimer, a Colombia specialist at Conciliation Resources, a London-based consultancy.
Right-wing parties bitterly opposed to a peace deal with leftist former rebel group FARC were leading Colombia's legislative elections Sunday but were set to fall short of a majority in Congress, partial results showed, AFP reprots.
The Marxist group, now transformed into a political party called the Revolutionary Alternative Common Force, failed to take a single seat in congressional elections as it polled less than one per cent on a day where the big victor was a hard-right critic of the peace accords. Final official results are expected later on Monday.
Meanwhile, the hardline Democratic Centre party - founded by former president Álvaro Uribe and fiercely critical of the peace deal - won 15.89%, the largest share.
Both left and right-wing coalitions chose their candidates in primaries over the weekend.
The party uses the same Spanish acronym, which now stands for the Common Alternative Revolutionary Force, and replaced its crossed-rifles insignia with a red rose.
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The FARC's Jorge Torres Victoria, who fought under the name "Pablo Catatumbo", was voting for the first time in his life, and hoping to win a Senate seat.
Opinion polls give the FARC little chance of adding to its 10 free seats, following a disastrous campaign during which its rebels-turned-politicians were largely drowned out by a tide of public revulsion over crimes committed during the conflict.
Its transition to a political party that contested Sunday's legislative elections is something of a triumph for the 66-year-old president, who won the Nobel Peace Prize in 2016.
Colombians went to the polls on Sunday to elect members of Congress in what President Juan Manuel Santos touted as "the most peaceful elections" in decades thanks to peace talks with the country's guerrilla groups.
But much of the peace agreement has already been implemented, including the rebels disarming and demobilizing.
Right-leaning candidates accuse Santos of failing to make a fair deal with the FARC - including by allowing ex-rebels to avoid jail sentences.
"The mere fact of not applying what has been signed would be enough for this agreement to be ineffective", said Frederic Masse, an expert on the conflict at Colombia's Externado University.