Maturino Resendiz had been ruled to be mentally competent to be executed, but his lawyers said he was delusional.
His lawyers and the local Mexican consul had asked the Supreme Court to stay the execution, but it refused.
Resendiz, 46 was sentenced to death in 2000 for killing a doctor and had been linked to 15 other murders as he crossed the US by train.
He was convicted of the rape and murder of Houston doctor Claudia Benton in 1998.
He either confessed or was linked by evidence to the brutal killings of 13 other people over a 16-month period ending in June 1999, as well as a murder in San Antonio in 1986.
'Won't die'
Many of the murders took place near railway tracks, including the double killing of Pastor Norman "Skip" Sirnic and his wife Karen in Weimar, Texas.
Weeks later, the body of 73-year-old Josephine Konvicka was found at her home on the town's outskirts.
Resendiz - who was on the FBI's 10 Most Wanted list - was, at one point, detained by US immigration authorities, but was deported to Mexico without questioning because of a computer error.
He surrendered to the police in July 1999 after his sister persuaded him to give himself up.
Resendiz's lawyers argued that he was a schizophrenic who believed he was half-man and half-angel, and was convinced he would not die but would return three days after his execution.
But at the end of a three-day hearing last week, State District Judge William Harmon said there was "no doubt in my mind" Resendiz understood his situation and the sentence he faced.
Defence lawyers' appeals were rejected by a federal judge in Houston and the Texas Board of Pardons and Paroles on Monday.
He was the 13th person to be executed in Texas this year.
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Glad to hear that he's dead.
