Two company executives acknowledged during a corruption probe in Brazil that Odebrecht made payments of between USD 50,000 and USD 100,000 a month in exchange for "permits" to build in territory held by the Colombian rebels, the weekly Veja reported.
Odebrecht began the payments in the 1990s after Revolutionary Armed Forces of Colombia (FARC) guerrillas kidnapped two Odebrecht executives.
The Brazilian conglomerate hired a US negotiating team that got the executives released, and then suggested regular payments as a way to prevent such problems in the future, Veja said.
The agreement allowed Odebrecht to complete a highway more than 500 kilometers long linking central Colombia with its Caribbean coastline, as well as other projects.
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Odebrecht, one of Latin America's largest building conglomerates, was at the heart of a scheme to bribe Brazilian state oil company Petrobras in exchange for inflated contracts.
Seventy-seven company executives have signed plea bargains with Brazilian prosecutors involved in the "Car Wash" probe and detailed their roles in the scheme. The testimony remains sealed, but is expected to send shockwaves through Brazilian politics when released.
Odebrecht admitted to paying USD 788 million in bribes across 12 countries and agreed with the US Justice Department to pay a USD 3.5 billion fine, a world record in foreign corruption cases.