As part of an agreement that would spare several of their relatives from prosecution, Gilberto and Miguel Rodriguez Orejuela entered their pleas before a Miami court on Tuesday.

The brothers founded the Cali cartel in the Colombian city of that name and ran a vast empire that supplied most of the cocaine sold in the United States in the early 1990s.

At its peak, the Cali cartel controlled 80 per cent of the world's cocaine trade.

Colombia extradited them to Florida in 2004 and 2005 to face charges of conspiring to import and distribute cocaine.

The judge sentenced the brother to 30 years in prison, effectively ensuring the two - both in their late 60s - will spend the rest of their lives behind bars.

The brothers also agreed to forfeit $2.1 billion of assets bought with illicit drug proceeds.

Miguel Rodriguez Orejuela apologised to his family and asked their forgiveness for the suffering he had caused them.

"I would also like to offer my apologies to the people of the United States," he said.

US prosecutors said the brothers had continued to run the family business from the Colombian prison where they were serving drug sentences.