He became the 531st inmate executed by Texas since the U.S. Supreme Court reinstated the death penalty in 1976, the most of any state.
"Yes, I would like to thank all of my supporters and loved ones," he was quoted by prison officials as saying in his last statement.
"I love you, Love y'all, always going to be with y'all. Thank you Warden," he said.Holiday was convicted of killing Tierra Lynch, 7; Jasmine DuPaul, 5; and Justice Holiday, 1, in a rural community about 160 km 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 he ignited, it said. The grandmother survived.
After watching the blaze, 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 U.S. 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 that included problems with his trial.