Robert Charles Gleason Jr., 42, had said he wanted to be put to death despite attempts by his former court-appointed attorneys to halt the execution and have him undergo a mental competency evaluation.
The attorneys had argued the time he spent in solitary confinement on death row left him unable to make rational decisions, a claim authorities rejected.
Gleason was pronounced dead at 9:08 p.m. (0208 GMT on Thursday), said Larry Traylor, a spokesman for the Virginia Department of Corrections. In his last statement, Gleason uttered the Irish Gaelic phrase "Pog mo thoin," or "Kiss my ass," Traylor said.
Gleason was the first inmate in the United States to be executed this year, according to the Death Penalty Information Center, a group that tracks capital punishment cases.
Virginia is one of nine U.S. states where inmates can choose to be executed either by electrocution or lethal injection, the more commonly used method to carry out executions in the United States.
Gleason was serving life in prison without parole for a 2007 murder when he admitted to using strips from bed sheets to bind and strangle Harvey Watson, a 63-year-old inmate at Virginia's Wallens Ridge State Prison in May 2009.
According to court documents, Gleason told authorities he timed the murder to coincide with the second anniversary of the previous homicide he carried out.
He admitted to tying Watson's hands without a struggle after telling him he had come up with a way for the two to escape. Court records show he taunted Watson before he strangled him by pressing a urine-soaked sponge onto his face and a sock into his mouth.
Gleason attacked another inmate in July 2010 at the maximum-security Red Onion State Prison while he waited to be sentenced for killing Watson, according to court records.
Gleason said he asked fellow inmate Aaron A. Cooper, 26, to try on a "religious necklace," which Gleason threaded through a wire fence separating the two while they were in solitary recreation pens.
Gleason testified that he choked Cooper through the fence "till he turned purple," waited for his skin color to return to normal, then choked him to death.
Cooper's mother has sued the Virginia prison system, accusing prison authorities of giving Gleason the opportunity to murder her son after Gleason told guards he planned to kill again.
During court proceedings, Gleason indicated he intended to keep killing unless he was given the death penalty, according to the state Attorney General's Office. Gleason told a federal judge earlier this month he did not want a lawyer and called for his execution to proceed.
His former lawyers said Gleason suffered from mental illness and had made several suicide attempts. Their final effort to halt the execution to allow for an evaluation of his mental competency was rejected by the U.S. Supreme Court on Wednesday.
It was the first time since March 2010 that someone was executed by electrocution in Virginia.
Last year, 43 people were executed in the United States, according to the Death Penalty Information Center.
(Editing by Kevin Gray and Eric Beech)