He then set their home on fire in Kennedale, a Fort Worth suburb.
Prosecutors say he killed his family because he wanted to run off with a woman he met at a convenience store.
Investigators say he confessed to the killings.
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Hummel, 45, who had been working as a hospital security guard, was convicted of capital murder in the deaths of his father-in-law and his 34-year-old wife.
Michael Mowla, Hummel's attorney, does not plan to file any last-minute appeals, saying all available legal avenues have been exhausted.
Appeals courts had rejected Mr Mowla's attempts to stop the execution over claims Hummel had not been properly assessed on whether he would be a future danger, which is one of the questions Texas juries must answer in death penalty cases.