Tommy Arthur was put to death by lethal injection at 12:15 a.m. (0515 GMT) in Atmore, Alabama, prison spokesman Bob Horton said, adding there were no complications during the execution.
Arthur said goodbye to his children before his execution, Horton said.
"I'm sorry I failed you as a father. I love you more than anything on earth," Arthur said, according to Horton.
Arthur was executed shortly after the U.S. Supreme Court lifted a stay on his execution as it considered arguments from his attorneys.
Arthur's lawyers argued that the use of the drug midazolam during the lethal injection was unconstitutional and questioned the legality of the state prohibiting a witness from having a cell phone to make a call if the execution went awry.
"When Thomas Arthur enters the execution chamber tonight, he will leave his constitutional rights at the door," Justice Sonia Sotomayor wrote in a dissent against the order to lift the stay.
Arthur had maintained his innocence for the 1982 murder of his girlfriend's husband.
Three juries had found him guilty of shooting Troy Wicker to death as he slept. Two convictions were overturned on constitutional grounds. After his third conviction in 1991, Arthur asked the jury to sentence him to death.
He fought his punishment since.
In November, the U.S. Supreme Court stayed Arthur's previous scheduled execution after he argued Alabama's lethal injection procedures amounted to cruel and unusual punishment.
In February, the court declined to hear Arthur's appeal, which focused on Alabama's use of the sedative midazolam. Examples of the drug's inability to render executions painless are increasing, Sotomayor said in a dissent.
In new appeals, Arthur said Alabama in December injected inmate Ronald Smith with painful execution drugs while Smith was still conscious.
State attorneys said evidence backs the drug protocol.
No physical evidence links Arthur to the murder, and Alabama has refused to allow DNA testing of a wig worn by the killer, his lawyers have noted.
Arthur was the 12th person executed this year in the United States and the first in Alabama, the Death Penalty Information Center said.
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