Barney Fuller Jr., 58, was pronounced dead at 7:01 p.m. CDT (12:01 a.m. GMT on Thursday) at the states death chamber in Huntsville after waiving his final appeals.
It was the seventh this year in Texas and the 16th in the United States, Reuters reported.
Fuller was sentenced to death after pleading guilty to capital murder in July 2004. A federal judge earlier this year ruled that he was competent to decide to forgo further appeals in his case.
The shooting rampage followed simmering disputes escalated between Fuller and his neighbors in rural East Texas, according to court documents.
Neighbors Nathan and Annette Copeland had complained to police that Fuller had shot their dog, fired at their house and fired at an electrical transformer for the residence.
The clashes escalated after Fuller told Annette Copeland "Happy New Year, Im going to kill you" over the phone and was charged with making a terroristic threat, according to court documents.
As his trial date was nearing in May 2003, Fuller went to the Copeland home and opened fire with an AR-15 rifle, the documents said.
After entering the home, Fuller shot and killed Annette, 39, and Nathan Copeland, 43, and wounded their teenage son, Cody. A 10-year-old daughter avoided injury, the documents said.
A few hours after the shootings, Fuller called 911 and confessed to the crime, according to the Texas attorney generals office.
In lieu of a final statement, the Texas Department of Criminal Justice quoted Fuller as saying: "I dont have anything to say. You can proceed Warden Jones."