The pair is facing charges of conspiracy to defraud the United States and conspiracy to encourage and induce an alien to reside unlawfully in the United States.
It was not disclosed how much the US resident made on her marriage-for-hire business.
But the pair "did knowingly and willfully combine, conspire, confederate, and agree with each other (...) to arrange fraudulent marriages," the indictment said.
Under the US Cuban Adjustment Act which dates back to the Cold War era, Cubans fleeing Communist rule who reach the United States - whether by plane, foot or boat - are allowed to stay and to work.
Those Cubans spotted and picked up at sea, in contrast, are returned to the Caribbean nation.
A quirk of the Cuban Adjustment Act is that it allows foreigners who wed a Cuban in the United States to get their US residency faster than if the foreign national weds a US-born American.
Piedra and De Moya face sentences of up to a decade in prison, if convicted.