Texas has carried out its 400th execution since the US Supreme Court reintroduced the death penalty in 1976.
Conner asked for forgiveness before he was put to his death
Johnny Ray Conner, 32, was put to death by lethal injection for the 1998 fatal shooting of a grocery store clerk.
Conner was pronounced dead at 1820 (2320 GMT), eight minutes after the lethal mix of drugs was injected.
Earlier this week, the EU urged Texas to end the "cruel and inhumane" practice. Texas's governor said it was a "just and appropriate" punishment.
Members of Conner's family and that of the victim, Kathyanna Nguyen, witnessed the execution through windows in the death chamber.
Before he was put to death, Conner - who had always maintained his innocence - asked for forgiveness and expressed love to his family and Ms Nguyen's family.
"What is happening to me is unjust and the system is broken," he said in his final statement.
His final words were: "I bear witness there is no God but Allah and the Prophet Muhammad. Unto Allah, I belong, unto Allah I return. I love you."
In 2005, a judge overturned Conner's death sentence and ordered a retrial, saying Conner's lawyers had been ineffective, but a federal appeals court reversed that decision in January.
On Tuesday, the EU expressed "great regret" at the execution.
"There is no evidence to suggest that the use of the death penalty serves as a deterrent against violent crime," it said.
But Texas Governor Rick Perry told the EU to mind its own business.
Robert Black, a spokesman for Mr Perry, told the BBC News website: "Two hundred and thirty years ago, our forefathers fought a war to throw off the yoke of a European monarch and gain the freedom of self-determination.
"Texans long ago decided the death penalty is a just and appropriate punishment for the most horrible crimes committed against our citizens.
"While we respect our friends in Europe... Texans are doing just fine governing Texas."
The Washington-based Death Penalty Information Center says the US has executed more than 1,090 prisoners since 1976.
Texas carried out more than a third of those.