Arthur, 75, was convicted in the 1982 murder-for-hire of romantic rival Troy Wicker.
The inmate, who was nicknamed the "Houdini" of death row because he'd had seven prior execution dates postponed, died by lethal injection at the Holman Correctional Facility at Atmore.
The Supreme Court issued a temporary stay Thursday, then lifted it later that night, leading to his execution.
"No governor covets the responsibility of weighing the merits of life or death; but it is a burden I accept as part of my pledge to uphold the laws of this state," Gov. Kay Ivey said in a statement.
"Three times Tommy Arthur was tried, convicted, and sentenced to death. Each time his case was reviewed thoroughly at every level of both our state and federal courts, and the appellate process has ensured that the rights of the accused were protected."
Arthur's lawyers had filed motions arguing that Alabama's method of execution was cruel and unusual, and that the attorneys should have access to a cellphone while witnessing the execution.
Before the Supreme Court decision, stay requests had been rejected by the 11th US Circuit Court of Appeals
, the Alabama Court of Criminal Appeals and the governor.
Arthur's lawyers had asked Ivey to delay the execution so DNA evidence could be examined from the killing for which he was sentenced to die.
Two executions were stopped when Arthur's convictions were overturned. Arthur has appealed other execution orders by arguing the combination of lethal injection drugs would cause him physical pain because of a heart condition.
Arthur was convicted of killing Wicker of Muscle Shoals by shooting him in the right eye on February 1, 1982, according to court documents.
He was a work release prisoner at that time. He had been convicted of killing his sister-in-law in 1977, also by shooting her in the right eye.
Arthur was in a romantic relationship with Judy Wicker, Troy Wicker's wife, the Birmingham News reported.
She initially told authorities that a burglar wearing a wig raped her and killed her husband, the Birmingham News reported. She later testified she paid Arthur $10,000 in life insurance money to kill her husband.
Arthur, who had pleaded not guilty, was first convicted in 1983, but that verdict was overturned on appeal, the News reported.
A 1987 conviction was overturned and he was convicted again in 1991.