"I’m sorry for what I did. I’m sorry for what happened, and I want to tell all of y’all, I love you and that … keep Jesus in your life, keep Jesus first," he said in his final words.
Thompson gasped loudly as the injection began taking effect, according to The Associated Press, before taking about a dozen breaths that turned into snoring sounds. He then stopped moving and was pronounced dead about 22 minutes later.
After witnessing the execution, Dennis Cain, whose son was killed by Thompson, said, "He’s in hell."
Harris County District Attorney Sean Tear, whose office prosecuted the case, said, "This chapter is closed."
"It was justice a long time coming," he added.
On the night of the murders, Thompson visited Hayslip’s apartment at 3 a.m. and got into an argument with Cain, according to court records. Thompson was told to leave the complex after police were called, but returned three hours later and shot the couple.
Cain died at the scene, while Hayslip died one week later.
Thompson’s original death sentence was later overturned, but a jury again sentenced him to die by lethal injection following a new punishment trial in November 2005.
Not long after being resentenced, Thompson escaped from the Harris County Jail in Houston and spent three days on the run before being caught.
He was arrested in Louisiana while trying to set up overseas wire transfers in an apparent attempt to flee to Canada.
About an hour before the scheduled execution, the U.S. Supreme Court issued a brief order rejecting a final appeal from Thompson. Earlier this week, the Texas Board of Pardons and Paroles denied Thompson’s request to commute his death sentence to a lesser penalty.
The Associated Press contributed to this report.