Richard Masterson, 43, was put to death by lethal injection at the state's death chamber in Huntsville. Masterson was pronounced dead at 6:53 p.m., the official said.
"Sending me to a better place. I am all right with this, you have to live and die by the choices that we make," Masterson was quoted by prisons officials as saying in his final statement.
The execution was the state's first this year and its 532nd since the U.S. Supreme Court reinstated the death penalty in 1976, the most of any state.
There were 13 executions last year in Texas, according to the Death Penalty Information Center, which monitors U.S. capital punishment.
Related: See notable death penalty cases:
Notable death penalty executions and people on death row
Texas executes man convicted of strangling female impersonator
Willie Francis, the first known incident of failed execution by lethal injection, was executed on May 9, 1947. He was sentenced to death for the murder of his former boss, Andrew Thomas.
John Wayne Gacy, a rapist and serial killer responsible for the sexual assaults and murders of at least 33 men, was executed in Illinois on May 10, 1994.
Ted Bundy, a kidnapper, rapist, and serial killer responsible for the assaults and murders of dozens of young women, was executed in in Florida on January 24, 1989. His actual victim count remains unknown.
Aileen Wuornos, a serial killer responsible for the deaths of seven men, was executed in Florida on October 9, 2002.
(AP Photo/Peter Cosgrove)
Charles Starkweather, a spree killer responsible for eleven murders, was executed in Nebraska on June 25, 1959.
(AP Photo/Don Ultang)
Timothy McVeigh, responsble for the Oklahoma City bombing, was executed in Indiana on June 11, 2001.
Thomas Provenzano, a convicted murderer responsible for shooting three people, was executed in Florida on June 21, 2000.
(AP Photo/Peter Cosgrove)
Gary Gilmore, responsible for the shooting deaths of two men, was executed in Utah on January 17, 1977.
Stanley "Tookie" Williams, founder and leader of the Crips gang responsible for several murders and other crimes, was executed in California on December 13, 2005.
(Photo by Justin Sullivan/Getty Images)
Teresa Lewis, convicted of murdering her husband and stepson, was executed in Virginia on September 23, 2010.
(AP Photo/Va Dept of Corrections)
William Bonin, a serial killer responsible for a minimum of 21 rapes and murders, was executed in California on February 23, 1996.
Dzhokhar Tsarnaev, responsible for Boston Marathon bombing, was sentenced to death on May 15, 2015.
(AP Photo/Federal Bureau of Investigation, File)
Nidal Malik Hasan, responsible for Ford Hood shooting, was sentenced to death on August 28, 2013.
(AP Photo/Bell County Sheriff's Department, File)
Joseph E. Duncan III, a convicted murderer and sex offender, was sentenced to death on August 27, 2008.
(AP Photo/Kootenai County First Appearance Video Court)
Death row prisoner Coy Wayne Wesbrook is photographed Wednesday, Feb. 3, 2016, at the Texas Department of Criminal Justice Polunsky Unit outside Livingston, Texas. Wesbrook, 58, is set for lethal injection March 9, 2016, for the November 1997 fatal shootings of his ex-wife and another man at her apartment in Channelview, just east of Houston. They were among five people killed during the shooting rampage. (AP Photo/Michael Graczyk)
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Masterson's lawyers had launched appeals with the U.S. Supreme Court to halt the execution, saying his due process rights were violated and Texas presented false and misleading evidence regarding the death of Darin Honeycutt, 35, who went by the stage name of Brandi Houston.
The Supreme Court denied the motions on Wednesday.
Pope Francis had been hoping for a reprieve, Catholic World News reported this week.
Masterson's lawyers said there was no struggle, no murder and the death was accidental. They also questioned the credibility of the medical examiner who called the death a homicide.
"Petitioner has never denied that he restricted the complainant's airflow, but only that it occurred during a consensual sexual encounter," they said in a court filing.
Texas prosecutors said that after Masterson killed Honeycutt, he left the state in the victim's car, which was found days later in Georgia being driven by a nephew of Masterson.
After fleeing to Florida, Masterson met a man in a bar frequented by gay men. The two went to the man's apartment and Masterson placed him a headlock, trying to strangle him, prosecutors said.
The man passed out and when he regained consciousness, he found that his car and wallet were gone, authorities said.
A Florida police officer ran across the stolen car at a mobile home park, which led to Masterson's arrest.
At his trial in 2002, Masterson, who has a long criminal record, did not admit to the murder.
He took the stand and said he was a danger to society, daring jurors to sentence him to death, which they did.