Ricky Bell, the warden at Riverbend Maximum Security Institution in Nashville, gives a tour of the prison's execution chamber on October 13, 1999.
Zagorski was condemned to die for his convictions in the April 1983 slayings of two men who had been shot and had their throats slit when they sought to buy marijuana from him in a drug deal-turned-robbery.
The execution was carried out shortly after the US Supreme Court on Thursday evening denied the inmate's request for a stay.
According to CBS affiliate WTVF, Miller has spent longer time than any other Tennessee inmate on death row.
Zagorski could be seen smiling as officials, preparing to carry out the first execution by electrocution in the USA since 2013, strapped him down.
Sotomayor said because of the unique litigation posture of the case, the denial of Zagorski's challenge "says nothing about the constitutional tolerability of the electric chair, which has raised concern in other forums".
"He did so not because he thought that it was a humane way to die, but because he thought that the three-drug cocktail that Tennessee had planned to use was even worse", Sotomayor said in the statement. Tennessee has used the chair only once in the last 58 years.
Edmund Zagorski is scheduled to be executed at chair 7 p.m. CDT Thursday at a maximum-security prison in Nashville. Only nine states allow the use of the electric chair to carry out a death penalty, but all of them have lethal injection as their primary method.
Death row inmates in the U.S. are given $20 for a meal of their choice prior to their execution. Zagorski's attorney, Kelley Henry, argued that the injection was too painful and his client had to choose the "lesser of two evils". Zagorski chose the chair because he thinks it will be quicker, but he maintains that both methods are barbaric.
Zagorski already had a petition pending in a different case.
The Tennessean reported that about eight of his family members and friends arrived at the Riverbend Maximum Security Institution in Nashville to view the killing. In 2013, Virginia killed a man convicted of two murders.
Leuchter, shunned for claiming there were no gas chambers at Auschwitz, said: 'What I'm anxious about now is Tennessee's got an electric chair that's going to hurt someone or cause problems.
Zagorksi was the first man executed in the electric chair in Tennessee since 2007.
Daryl Holton chose to die in the electric chair in 2007.
The last person to be executed by electrocution in the US was Robert Gleason, who was put to death in Virginia in 2013.
Officials initially had meant to perform a lethal injection, which has become more common, but Zagorski challenged the state's use of a three-drug cocktail that includes the controversial sedative midazolam.
Despite the decision, Zagorski's attorneys said he was forced into a "terrible choice", arguing that electrocution though "relatively fast" is also "dreadful and grim".