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.
He had also murdered Georgia civil rights lawyer Robert Robinson.
In last-hour appeals, Moody's lawyers had asked the US Supreme Court to stay his execution in order to review whether his federal sentence, which was handed down first, could be interrupted.
Early Thursday afternoon the Alabama Supreme Court denied a stay of execution in Moody's case.
The court is expected to rule later whether the execution plan can proceed.
The non-profit Death Penalty Information Center says Moody became the oldest inmate put to death in the United States since the resumption of US executions in the 1970s.
Moody has maintained his innocence insisting he was framed.
Alabama state attorneys had argued that the federal government had agreed to the transfer.
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.
"He was also convicted of a similar pipe bomb death of a Georgia attorney", according to a statement from the state's attorney general, Steve Marshall.
He is now the oldest inmate put to death in the US since executions were resumed in the 1970s. Prior to that, there had been none in the modern era of US executions, according to the Death Penalty Information Center.
Lawyers for Moody asked the Supreme Court to spare Moody's life based on his transfer from the federal court system to Alabama's but this application failed.
The execution was carried out at 8:17 p.m., according to the Department of Corrections.
Zeigler said Moody's long period on death row also meant taxpayers had to foot the bill for his room, board and medical expenses.
U.S. Attorney Jeff Sessions has told Alabama officials that they can have full custody of Moody to carry out his death sentence.
It was the eighth execution to be carried out in the U.S. in 2018, CNN reported.
His complex case drew in people who would become household names of United States law enforcement: Louis Freeh, a future Federal Bureau of Investigation director; Robert Mueller, the special counsel investigating Russian interference in the 2016 presidential election; and Jeff Sessions, now the USA attorney-general.
One way that Alabama lawmakers want to expedite the execution process is to allow the use of nitrogen gas to execute inmates.
The execution is set to happen almost 30 years after Walter Leroy Moody Jr. killed a federal judge with a bomb mailed to his home.
Up until Thursday evening, John Nixon was the oldest prisoner executed when he was put to death at the age of 77 in December 2005 in Mississippi.