Mark Stroman, a Texas death row inmate, shot at least three men he mistook for Arabs in the weeks after the attacks, killing two of them.
He was convicted of killing Vasudev Patel, 49, during the attempted robbery of a convenience store near Dallas in October 2001. He was also charged in the fatal shooting of Waqar Hasan, 46, a Muslim born in Pakistan.
He was executed after the US Supreme Court on Wednesday rejected a last-minute appeal by one of his victims to save his life.
The lone survivor, Rais Bhuiyan, a native of Bangladesh, had sued to stop the execution, saying his religious beliefs as a Muslim told him to forgive.
Earlier Stroman had said his 2001 Dallas-area shooting rampage was in retaliation for the September 11 terrorist attacks. He had described the attacks as a patriotic response to terrorism.
Stroman blamed the shootings on the loss of a sister in the collapse of one of the World Trade Center towers, although prosecutors said in court documents there''s no firm evidence she ever existed.
"I wanted those Arabs to feel the same sense of vulnerability and uncertainty on American soil much like the mindset of chaos and bedlam that they were already accustomed to in their home country," he said on a website devoted to his case.
Patel, whose death put stroman on a death row, had moved from India to Texas in 1983, and was a naturalised US citizen.
Stroman described his victims as "perched behind the counter here in the Land of Milk and Honey..this foreigner who''s own people had now sought to bring the exact same chaos and bewilderment upon our people and society as they lived in themselves at home and abroad."
But he added he had made a "terrible mistake out of love, grief and anger" and had destroyed his victims' families "out of pure anger and stupidity.
He also said he wanted to spend time with the convict to learn more about why the shootings occurred.
"I'm not the monster the media portrays me," he has said.
Stroman was free on bond for a gun possession arrest during the time of incident. He had previous convictions for burglary, robbery, theft and credit card abuse, served at least two prison terms and was paroled twice.
Stroman's lethal injection would be the eighth this year in Texas. At least eight other inmates in the nation''s busiest death penalty state have execution dates in the coming weeks.