The magazine Cambio reports that 15 heirs of late cocaine drug lord Gonzalo Rodriguez Gacha, known as "the Mexican," avoided prosecution by paying off the US District Court in Jacksonville, Florida.
Gacha, one of Colombia's biggest and bloodiest traffickers, was killed by Colombian police in 1989.
Cambio said the deal came to light in February when a Colombian intelligence unit discovered files belonging to the family.
They included a 10-year-old letter guaranteeing them immunity from prosecution on drug-smuggling charges.
The US$83 million moved through 24 bank accounts around the world, the magazine said. The US court receiving the final US$1.3 million payment from a bank on the Isle of Man on January 31.
Cambio, which is supported by Nobel prize winning author Gabriel Garcia Marquez, published an image of the letter with the article.
Cambio also said it had confirmed parts of the story with US prosecutor Charles Wilson, several magistrates, and the Gacha family's US lawyer, Richard Hamar, who called the use of pressure in the deal "immoral and unconstitutional".
The magazine said that the Colombian government had heard no more than rumors about the deal.
Former Colombian vice president Humberto de la Calle told Cambio, "The average Colombian looks askance at the fact that after so many years of suffering because of drug trafficking and terrorism generated by the consumers of cocaine in the United States, traffickers and their heirs end up negotiating with the courts of that country and receive short sentences and even immunity simply because they handed over money."