Kelly Gissendaner, the only female death row inmate in the state, was killed by lethal injection and pronounced dead at 5.21am BST on Wednesday.
Gissendaner, 47, was the first woman put to death in the southern state in more than 70 years.
She was convicted of murdering her husband in February 1997 after she conspired with her lover, who stabbed Douglas Gissendaner to death.
She requested a final prayer before she died, according to prison spokeswoman Lisa Rodriguez-Presley.
State officials had been asked by Pope Francis to give her clemency.
In a letter from his representative in the US, Archbishop Carlo Maria Vigano, he pleaded with the state "to commute the sentence to one that would better express both justice and mercy".
It read: "While not wishing to minimize the gravity of the crime for which Ms. Gissendaner has been convicted, and while sympathizing with the victims, I nonetheless implore you, in consideration of the reasons that have been presented to your Board, to commute the sentence to one that would better experess both justice and mercy."
He also referenced the Pope's historic speech to Congress which called for an end to the death penalty across the globe.
Ms Gissendaner, who converted to Christianity whilst in prison, cried as she waited to be put to death.
"Bless you all," she said, "tell the Gissendaners I am so, so sorry that an amazing man lost his life because of me. If I could take it all back, I would."
Gissendaner also addressed her lawyer, Susan Casey: "I just want to say God bless you all and I love you, Susan.
"You let my kids know I went out singing Amazing Grace."
She converted to Christianity whilst in prison and studied for a theology degree.
More than 100 people, including clergy members, gathered outside the prison to support her.
Revd Della Bacote, a chaplain at Saint Thomas Hospital in Nashville, joined the crowd showing its support.
She had previously spent several hours with Gissendaner on Tuesday afternoon talking and praying.
"She was at peace with whatever was to come," Revd Bacote said.
Gregory Owen, the man who carried out the fatal stabbing, is serving a life sentence and will become eligible for parole in 2022 because he agreed a plea deal to testify against her.
Mr Gissendaner's family said in a statement that he was the victim and that his wife, Kelly Gissendaner, received an appropriate sentence.
It read: "As the murderer, she's been given more rights and opportunity over the last 18 years than she ever afforded to Doug who, again, is the victim here.
"She had no mercy, gave him no rights, no choices, nor the opportunity to live his life."
In 1997 Owen ambushed Douglas Gissendaner at his home, forced him to drive to a remote area and stabbed him multiple times, prosecutors said.
Gissendaner's lawyers have said she that she had undergone a spiritual transformation in prison and had been a model prisoner who had shown remorse.