The Mexicans were arrested last year after Nicaraguan officers found bundles of cash hidden in their phony TV news vehicles.
In January, a Nicaraguan judge sentenced them to 30 years, but those sentences were reduced to 18 years on appeal.
Nicaragua has an agreement with Mexico allowing prisoners to serve out sentences in their home countries.
Nicaraguan Supreme Court chief justice Alba Luz Ramos says the inmates asked for the transfer, noting it will free up prison space in Nicaragua.