Raphael Holiday’s other two victims were his step-daughters, who were aged five and seven.
The 36-year-old was put to death by lethal injection and pronounced dead at 8:30 pm (0230 GMT Thursday), said Jason Clark, a spokesman for the Texas Department of Criminal Justice.
Holiday had been in a dispute with his wife and had been ordered by a court not to see her.
But in September 2000 he ignored that injunction and broke into her home in Madison County. His terrified wife fled to seek help.
Threatening the girls’ grandmother with a gun, Holiday forced her to pour gasoline throughout the home, which was then ignited in flames.
Holiday was the 13th inmate executed this year in Texas, which has accounted for half the executions so far in 2015 in the United States, the Death Penalty Information Center said.