Raphael Holiday was put to death by lethal injection at the state's death chamber in Huntsville and pronounced dead at 8:30pm on Wednesday (local time), a prisons official said.
He became the 531st inmate executed by Texas since the US Supreme Court reinstated the death penalty in 1976, the most of any state.
Holiday was convicted of killing Tierra Lynch (7), Jasmine DuPaul (5) and Justice Holiday (1) in 2000 in a rural community about 160km northwest of Houston.
He had been living with Tami Wilkerson, his common law wife at the time, until she secured a restraining order against him for sexually assaulting Tierra, according to the Texas Attorney General's office.
About six months later, Holiday, who had attempted to reconcile with Wilkerson, returned to the house and forced the girls' grandmother at gunpoint to douse the home with gasoline, which ignited, it said. The grandmother survived.
After watching the house burn, he fled the scene in a vehicle and was caught after a high-speed chase with police. The bodies of the three girls were later found huddled together in the charred remains of the home, the office said.
The US Supreme Court denied a request filed by a new lawyer for Holiday, who argued his federally appointed counsel had acted against his wishes and abandoned further rounds of court filings to spare his life. Those lawyers told their client further appeals were hopeless and they did not want to provide false hopes, court papers showed.
The Supreme Court in June denied a request from Holiday's federally appointed lawyers to put a hold on the execution on grounds including problems with his trial.
