Cheng Chieh, 23, was anaesthetized then shot three times by a firing squad at a jail outside Taipei a little before 9:00 pm (1300 GMT), deputy justice minister Chen Ming-tang told reporters.
"Death was the only way to show publically that justice had been served and to relieve the sorrow and pain of victims' families," he said.
Cheng was sentenced to death last year for killing four people and injuring another 22, in the first fatal attack on the capital's subway system since it launched in 1996.
Among the victims of the attack in May 2014 was a man named Hsieh Ching-yun. His mother said she was "glad" Cheng had been executed.
"Losing my son is a pain that will last forever, for the rest of my life," she told the TVBS cable news network.
Prosecutors sought the death penalty for Cheng, saying psychological evaluations showed that he was not suffering from any mental disorder when he committed the crime.
Cheng, who pleaded guilty to the charges, was expelled by his university after the attack and was described by prosecutors as "anti-society, narcissistic, immature and pessimistic".
Cheng's parents had asked for him to be sentenced to death, calling their son's actions "unforgivable".
The incident shocked Taiwan, otherwise proud of its low levels of violent crime, and resulted in several minor injuries as edgy commuters fled trains over false alarms in the following week.
There are currently 42 prisoners on death row in Taiwan, all of whom will face a firing squad when they are executed.
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