At Latin America’s biggest construction company, bribing government officials around the world became so common that a division was created devoted to tracking and facilitating kickbacks.

When wire transfers were inconvenient, workers in this division at Odebrecht of Brazil would organize deliveries of cash-stuffed suitcases to secret locations.

The scheme lasted more than two decades and involved bribes to government officials in a dozen countries across three continents, but eventually it came undone. On Wednesday, Odebrecht and its affiliated petrochemical firm, Braskem, pleaded guilty in Federal District Court in Brooklyn to charges that they paid hundreds of millions of dollars in bribes. Together the companies will pay at least $3.5 billion in penalties in a case brought by authorities in the United States, Brazil and Switzerland.

It is the biggest penalty for a violation of the Foreign Corrupt Practices Act of 1977, surpassing a $800 million penalty paid by Siemens in 2008 to authorities in the United States. American officials said on Wednesday that their investigation was continuing and that individuals could also be prosecuted.