Jonathan Green received a lethal injection Wednesday night, KUT (national public radio) News, Austin, Texas, reported. The warrant for his execution was set to expire at midnight.
Green's execution was halted Monday by a federal judge who ruled that Green's due process was violated during his competency hearing.
Then, the Fifth U.S. Circuit Court of Appeals overturned that decision.
The U.S. Supreme Court then rejected a request to review the appeals court's decision.
Green, 44, was convicted of the abduction, rape and murder of a 12-year-old girl in 2000.
On June 21, 2000, Green kidnapped the girl from her home in Montgomery County, Texas, prosecutors said. Green took the victim to his residence, where he killed her by strangling her to death. The victim was also sexually assaulted.
Green was the 10th inmate put to death in Texas this year.