Donnie Lance, 66, received a lethal injection at the Georgia Diagnostic and Classification Prison in Jackson at 9:05 pm (0205 GMT Thursday), according to the Georgia Department of Corrections.
He was sentenced to death in 1999 for shooting his ex-wife's new partner in the head two years earlier and then beating her to death with the gun.
Lance had repeatedly threatened to kill his wife if she left him, according to prosecutors, and continued his threats after their breakup. He even sought advice about how much it might cost to put out a hit on the new couple.
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Lance denied his guilt in the case, and his lawyers say no proof showing he committed the crimes was presented at the trial.
In trying to overturn his conviction over the last two decades, Lance's defence team had unsuccessfully asked that DNA evidence be re-examined and that a new trial be held.
They hoped the US Supreme Court would grant a last-minute stay of execution in light of those requests, but the court denied the stay Wednesday just before the execution was scheduled.
Lance is the second person executed in the United States this year, after a man in Texas earlier this month.
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