Christopher Wilkins, 48, was executed by lethal injection at 6pm on Wednesday in the state's death chamber in Huntsville.
The execution is the 539th in Texas since the US Supreme Court reinstated the death penalty in 1976 - the most of any state.
The planned lethal injection came as the number of US executions fell to a quarter-century low in 2016.
Factors for the decline include high costs of prosecutions, sales bans on lethal injections drugs and increased use by juries of life without parole as a sentence.
Lawyer for Wilkins had filed an appeal with the US Supreme Court seeking to halt the execution, arguing he had ineffective counsel and was unlawfully denied funding necessary for an adequate defence.
But about three hours ahead of the scheduled execution time, the court rejected the appeal.
Wilkins was convicted of killing Willie Freeman, 40, and Mike Silva, 33, in 2005 in the Fort Worth area and dumping their bodies.