BOGOTA, Colombia—It was one of the biggest corporate corruption scandals in history, and its web of connections still hasn’t been fully untangled across Latin America. Having paid out hundreds of millions of dollars in political bribes in order to secure lucrative contracts at home and abroad, the Brazilian construction giant Odebrecht continues to upend politics, lately in Ecuador and Peru.

But things are picking up in Colombia, too. In August, Colombia’s Supreme Court called on President Juan Manuel Santos and several former ministers to testify about Odebrecht bribes to the Colombian government that the attorney general’s office says exceed $27 million. Investigations have already revealed that both of Santos’ election campaigns, in 2010 and 2014, received money from Odebrecht. ...