Efrain Antonio Campo Flores, 31, and Francisco Flores de Freitas, 32, were convicted by a New York jury last year after being arrested in a US sting operation Haiti in 2015.
District Judge Paul Crotty imposed the 18-year jail term in a Manhattan federal court on Thursday and fined each cousin $50,000.
US government prosecutors had requested a 30-year sentence, arguing that they believed they could operate with impunity as members of the most powerful family in Venezuela.
Defense lawyers sought the minimum 10-year penalty and the two cousins apologized in court, Flores de Freitas breaking down into tears at the mention of his nine-year-old son and asking the judge for a chance to repair his mistakes.
"If they were not from Venezuela but from the Dominican Republic or the Bronx this would be a 10-year case," said defense attorney David Rody.
But "they're not the (Venezuelan) president and they should not bear the brunt of the government's ire towards Venezuela," he added.
The judge ruled that the two defendants seemed "more concerned about the impact on the family than on violating the law in the United States."
He noted that "opportunities for visitation from Venezuela will be very limited" given US travel restrictions imposed on many Venezuelans with ties to President Nicolas Maduro's government.
Their arrest and trial fanned tensions in already fraught US-Venezuelan relations, with Washington at loggerheads with Maduro and the South American oil giant mired in economic crisis.
The cousins, who are sons of brothers of First Lady Cilia Flores, were convicted of plotting to smuggle 800 kilos (1,760 pounds) of cocaine into the United States, as well as manufacturing and distribution with the intent to import.
The Venezuelan government says they were framed.
Lawyers for both defendants argued that they fell into a trap set by the US Drug Enforcement Administration in a sting operation that offered $20 million for the drugs.
US prosecutors say the men believed they were above the law as relatives of Maduro. Their aunt, Cilia Flores, was speaker of the National Assembly from 2006 to 2011.
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