Miller, 65, was convicted for the 1999 murders of three men, including two co-workers, in a shooting spree at two offices in Pelham, Alabama.
His victims were Lee Michael Holdbrooks, Terry Lee Jarvis and Christopher Scott Yancy.
Miller was taken into the execution chamber on Thursday evening at the Holman Correctional Facility in Atmore, and was pronounced dead at 6:38pm, Alabama Governor Kay Ivey said in a statement.
He shook and trembled on the gurney for about two minutes with his body at times pulling against the restraints. That was followed by about six minutes of periodic gasping breaths.
"Tonight, justice was finally served for these three victims through the execution method elected by the inmate," Ivey said.
"His acts were not that of insanity, but pure evil. Three families were forever changed by his heinous crimes, and I pray that they can find comfort all these years later."
In January, Alabama executed Kenneth Smith, also convicted of murder, by nitrogen asphyxiation, the first use of a new execution method since lethal injections began in the US four decades ago.
The state called its new protocol "the most painless" execution method yet, and predicted that Smith would lose consciousness and suffocate within a few seconds of pure nitrogen flowing through an industrial-safety respirator mask strapped to his face.
That did not happen.
Multiple witnesses, including five journalists and members of Smith's family, saw Smith heaving against his restraints and convulsing as the nitrogen flowed, and it appeared to take him several minutes to lose consciousness.
The administration of US President Joe Biden, a Democrat who promised to abolish the death penalty, said it was "deeply troubled" by the new method.
It has been condemned by senior UN human rights officials, who say it may amount to torture or cruel and inhuman treatment.
Alabama has defended the method, with Attorney General Steve Marshall calling Smith's death a "textbook" execution.
After Smith's execution, Miller sued Alabama over fears that its asphyxiation method could violate a constitutional ban on cruel and unusual punishments.
He sought assurances that the mask would be properly fitted and that its seal be tested to ensure no oxygen seeps in, prolonging his death or even averting it entirely and leaving him alive with brain damage.
His litigation ended in a confidential settlement. The Alabama Department of Corrections declined to say if it made any changes to its gassing protocol.
Alabama has offered to help others adopt nitrogen-asphyxiation executions, saying they are a simpler alternative for states struggling to find lethal-injection drugs.
Advocacy groups against capital punishment have long pressured pharmaceutical companies to forbid their drugs be used in executions, and have turned their attention to nitrogen suppliers and mask makers, including the maker of the Allegro Safety mask Alabama acquired for its executions.
- with AP
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