One was shipped to the Alabama home of Robert Vance, a federal judge.
Prosecutors believed Moody disguised his motive by using the name of a fictitious group when he vowed to kill judges and railed against African-Americans and the Atlanta-based 11th Circuit's treatment of them.
If his execution is carried out, Moody will be the oldest inmate put to death since executions resumed in the U.S.in the 1970s, according to the non-profit Death Penalty Information Center. Package bombing done by Moody was a revenge story on the legal system. Moody, he said, fits the definition of a psychopath.
Federal officials began to focus on Moody after an investigator described one of the bombs to a chemist with what was then known as the Bureau of Alcohol, Tobacco and Firearms, who sketched the device on a napkin and noticed its similarity to one Moody had built in 1972. Prosecutors said Moody, who had attended law school, had a grudge against the legal system because the 11th Circuit refused to overturn a 1972 pipe-bomb possession conviction that prevented him from practising law.
The previous record holder for oldest inmate to be put to death in modern times was set by John Nixon, a 77-year-old MS man who was convicted of murdering a woman in 1985. For killing Vance, an Alabama court sentenced Moody to death in 1996.
It has been almost 30 years since Robinson's death.
As his scheduled lethal injection neared, Moody sought to have it stayed, arguing against Alabama's ability to execute him because he was first sentenced on federal charges. Moody had mailed two other bombs to the NAACP office in Jacksonville, Florida but they were intercepted and did not explode.More news: Feds Seized Recordings From Michael Cohen
"The murder of Judge Vance was unprovoked and inexcusable".
Moody maintained his innocence to the end. In a recent letter to Mr Vance Jr, he wrote, "Had my Dad been murdered, I would want to know who had done it".
"He was a great judge, a great lawyer before that, and a great father", he said earlier as the execution loomed.
The younger Vance made no plans to witness the execution. The nation's high court had no comment on those last-minute appeals Thursday.
Moody's reign of terror - deadly bombings and thwarted attacks in three Southern states, as well as menacing letters to judges and the media - raised fears of racial violence and unsettled the federal judiciary.
The younger Vance said his father also upheld death sentences because he believed in following the law. Alabama Attorney General Steve Marshall commented on the execution, saying that justice had been served in the case.
He said he had to make peace with his father's death, but said he has no doubt that Moody is guilty.