John Gardner, 64, received a lethal injection at the state penitentiary in Huntsville for the January 2005 fatal shooting of Tammy Gardner. Prosecutors said the couple was getting divorced when Gardner broke into his wife's North Texas home and shot her in the head as she lay sick in bed. She died two days later at a hospital.
Asked if he had any last words, Gardner apologized to his wife's son, daughter and mother.
"I would like to say sorry for your grief," he said. "I hope what I'm doing today will give you peace, joy, closure, whatever it takes to forgive. I am sorry. I know you cannot forgive me, but I hope one day you will."
Gardner became the first inmate put to death this year in Texas and the U.S. Seven other executions are scheduled in the next few months in Texas.
His appellate attorneys had petitioned the U.S. Supreme Court to intervene, alleging that his trial lawyers had failed to present evidence that Gardner suffered from "abandonment rage," a condition Gardner claims causes men to kill their female companions with excessive force when faced with abandonment.
The Supreme Court denied the petition on Monday. Seth Kretzer, one of Gardner's attorneys, said he was "deeply saddened" by the Supreme Court's decision.
Prosecutors at trial described the marriage between John and Tammy Gardner as short but violent. She was Gardner's fifth wife. The couple married in 1999.
"He was a classic abuser," said Curtis Howard, who was one of the prosecutors for the Collin County District Attorney's Office.
Friends and family of Tammy Gardner, 41, testified that she lived in constant fear of John Gardner, who would hit and choke her and threaten her with a gun. She had wanted to divorce him but was afraid he would kill her if she left, they said.
In December 2004, Tammy Gardner filed for divorce after borrowing money from her company to do so. But around midnight on Jan. 23, 2005, just 15 days before the divorce became final, John Gardner drove from Mississippi, broke into her home in Anna, Texas, and shot her in the head.
Tammy Gardner called 911 and was hospitalized. She soon went into a coma and was taken off life support two days later.
Lydia Brandt, one of Gardner's attorneys, had argued that if evidence of abandonment rage would have been presented at trial, it would have humanized him, "thereby providing a basis for a sentence of less than death."
Howard said the theory would not have made a difference at trial because abandonment was not related to all of his many acts of violence, which included shooting his second wife, who was pregnant at the time and later died from resulting injuries, abducting his third wife at knifepoint and savagely beating his third wife's daughter.
The Associated Press contributed to this report.