Humberto Leal Garcia, 38, died just after 6 p.m. CDT at the state prison in Huntsville, the San Antonio Express-News reported. He was executed for raping and killing Adria Sauceda, 16, in San Antonio in 1994.
"I am truly sorry. Viva Mexico! Let's get this show on the road," he said as his last words.
The execution came hours after the U.S. Supreme Court, in a 5-4 ruling, refused to stop the execution. The Supreme Court decision, which was not signed, cleared the way for the execution, Politico reported.
Texas Gov. Rick Perry has declined to intervene, ignoring appeals from President Barack Obama and Perry's fellow Republican, former President George W. Bush, the Houston Chronicle reported.
Leal had lived in the United States since he was 2. In 2004, the International Court of Justice in The Hague, Netherlands, ruled U.S. law enforcement agencies violated the rights of Leal and 50 other non-citizen death-row inmates by failing to notify them of their right to see consular representatives or notifying embassies of their arrest.
The U.S. Supreme Court ruled the Vienna Convention on Consular Relations does not bind the states because Congress has not passed a law requiring them to honor it.
Obama urged Texas to postpone Leal's execution while Congress considers a law introduced by Sen. Pat Leahy, D-Vt., that would extend the treaty to the states.