Sirnic and his wife Karen Sirnic were bludgeoned to death with a sledgehammer in a parsonage of the United Church of Christ in Weimar.
Police found Resendiz in 1999 with the help of his sister Manuela, who feared her brother might kill more people or be killed himself.
She persuaded her brother to surrender to authorities voluntarily, a procedure that took place on an international bridge connecting El Paso, Texas, to Ciudad Juarez, Mexico.
As many as 60 people were executed in the United States last year -- 19 of them in Texas. Resendiz was the 13th convict to be put to death in Texas this year.
Mexican nationals make up a significant segment of US death row, with 52 of them currently awaiting execution in various penitentiaries.
Six Mexicans have been executed in the United States since 1976, when the US Supreme Court reinstated the death penalty, each time triggering protests from the Mexican government.
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