The BBC reports:
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."