Edgar Tamayo, 46, who was denied an 11th-hour stay of execution by the US Supreme Court, was pronounced dead at a state prison in Huntsville, Texas.
The Mexican government had called on Texas to halt the execution, calling it a violation of international law, and US Secretary of State John Kerry had asked Texas Governor Rick Perry to consider a stay.
Tamayo was convicted of shooting Houston police officer Guy Gaddis to death in 1994 after he had arrested him on suspicion of robbery.
While handcuffed in the police car, Tamayo pulled a pistol and shot Gaddis, 24, three times in the back of the head. Tamayo kicked open a window and ran away from the car but was arrested again a few blocks from the scene.
The Mexican government claimed Tamayo was not informed of his right to diplomatic assistance in the case, a guarantee enshrined in an international treaty known as the Vienna Convention on Consular Relations.
In 2004, the UN's International Court of Justice ordered the US to reconsider the convictions of 51 Mexicans, including Tamayo, who had been sent to death row without being informed of their consular rights.
Tamayo was in the US illegally at the time of his arrest.