Muhammad was pronounced dead at 2111EST
The man behind the 2002 sniper attacks in and around Washington DC has been executed after a final appeal was thrown out.
John Allen Muhammad's lawyers say he was mentally ill, but Virginia Governor Tim Kaine rejected a plea for clemency.
On Monday, the US Supreme Court quashed an appeal for a stay of execution.
Muhammad, 48, was injected with a lethal drug for the murder of Dean Harold Meyers, one of 10 people killed during the attacks.
Muhammad's accomplice, Lee Boyd Malvo, who was 17 at the time of the shootings, is serving a life sentence in jail.
The pair killed 10 people during three weeks of attacks in Maryland, Washington and Virginia.
Witness describes sniper's final moments
Muhammad was put to death at the Greensville Correctional Center in Jarratt, Virginia.
The procedure took five minutes, and Muhammad died at 2111 (0211 GMT), Larry Traylor of the Virginia Department of Corrections said.
Muhammad did not speak before it began, and seemed quiet and relaxed, Mr Traylor said.
"Mr Muhammad was asked if he wished to make a last statement. He did not acknowledge us or make any statement whatsoever," he said.
He had, Mr Traylor added, been motionless, with his head slightly tilted to the right as the drug was injected.
His lawyer said he had eaten chicken in red sauce, followed by strawberry cakes, for his final meal.
Before the execution J Wyndal Gordon, the state attorney appointed to represent Muhammad, said that he would die "with his head held high and no remorse, maintaining his innocence".
He was, said his lawyer, "a martyr for everything that's wrong with the death penalty".
After the execution, he extended condolences to the victims' loved ones, but also to Muhammad's relatives.
"It's just a tragic situation all around."
Muhammad's legal team says the ex-soldier suffered from Gulf War Syndrome.
Lawyer Jonathan Sheldon told the BBC's World Today: "A psychiatrist examined him and said he's paranoid and psychotic and delusional and gave many examples."
Mr Sheldon also said brain scans of Muhammad had revealed malformations linked to schizophrenia.
The shootings left the Washington area gripped by fear, with victims attacked while shopping, outside schools, or just sitting and reading.
Mr Meyers was shot at a petrol station in Manassas, Virginia.
A skilled marksman, Muhammad picked off his targets using a sniper rifle, always with a single round and from a distance.
After three weeks, he was arrested at a truck stop, along with Malvo.
Seven years on, Washington residents recall sense of fear while sniper was on the loose
Prosecutors say Muhammad never showed remorse.
In addition to the 10 people they killed around the Washington area, the pair were suspected of murders in other states, including Louisiana, Alabama and Arizona.
Cheryll Witz was one of several victims' relatives who went to watch Muhammad's execution.
Malvo said he had shot her father, Jerry Taylor - at Muhammad's direction - on an Arizona golf course in March 2002.
"He basically watched my dad breathe his last breath," she told the Associated Press news agency.
"Why shouldn't I watch his last breath?"
THE SNIPER SHOOTINGS
1 and 2. A shot fired in Aspen Hill, north of Washington DC on 2 October. James D Martin is later killed in Wheaton
3, 4, 5, 6 and 7. The following day, James "Sonny" Buchanan, Prenkumar Walekar, Sarah Ramos, Lori Ann Lewis-Rivera and Pascal Charlot are all shot dead in areas to the north of the city
8. On 4 October a woman is shot at a mall in Fredericksburg, Virginia
9. On 7 October a 13-year-old schoolboy is shot at Benjamin Tasker Middle School in Prince George County
10 and 11. Dean Harold Meyers is shot dead in Manassas, Virginia on 9 October. Two days later, Kenneth H Bridges is killed near Fredericksburg
12. Linda Franklin is shot dead at a shopping centre in northern Virginia on 14 October
13. A 37-year-old man is shot in Ashland, south of Washington on 19 October
14. Conrad Johnson is killed on 22 October in the Aspen Hill area