McVeigh was convicted of all 11 counts of murder and conspiracy, including the killings of eight US government employees, in the worst act of terrorism on American soil.
The verdict was followed by emotional scenes outside the court building in Denver, Colorado, and at the site of the bombing in Oklahoma City where survivors and relatives of McVeigh's victims, who included 19 children, had gathered.
His fate lies with the jury which must weigh whether to sentence him to death. Jurors could reconvene as early as tomorrow. Some survivors and relatives will present "victim impact statements" to the court, in a last outpouring of personal grief, as McVeigh's lawyers plead for his life. If the jury chooses the death penalty - in a state that has not used it for 30 years - three-quarters of Americans would agree, according to a Newsweek magazine poll.
However, Buddy Welch, whose sister Julie died, took a rare stand against execution. It would have "no redeeming value", he said. "If he's executed, he can never talk."
Prosecutors had described McVeigh, 29, as a "domestic terrorist", who blew up the federal government Alfred P Murrah building in an attempt to start the "second American revolution" and to see "blood flow in the streets of America". Within two days of the bombing the Gulf war veteran was identified as the man who rented a truck whose severed axle was discovered near the building after the bombing. The FBI found its chief suspect was already in jail - he had been arrested for a traffic offence in his getaway car.
The verdict promised to be an immense relief both to prosecutors and the FBI, as well as the bomb victims. Though McVeigh's alleged co-conspirator, Terry Nichols, must still face trial, it was McVeigh who was said to have picked the target and driven the truck containing the bomb to the spot. The jury yesterday found him guilty of plotting and carrying out the use of a weapon of mass destruction. As the jury was deliberating, Oklahoma authorities announced they were setting aside $650,000 (pounds 400,000) to prosecute McVeigh, whatever the result, on state charges of murdering 168 people.
The bombing in Oklahoma City marked the rise in the United States in 1994 of the so-called militias, far-right groups who believed the Government so overstepped its authority that they must arm against it. McVeigh was not an active member but was inspired by their beliefs. After the bombing, mainstream support for these groups rapidly fell away.
McVeigh was also obsessed with the government showdown with the Branch Davidian sect in Waco, Texas, in which 80 people died. He blamed the government and during the trial the star prosecution witness, Michael Fortier, testified that McVeigh thought its assault on Waco was planned in the Murrah building. It was bombed two years to the day after Waco.
The US President, Bill Clinton, said yesterday's verdict brought a "very important and long overdue day" for the victims' families.
"No single verdict can bring an end to your anguish," he told them, "but your courage has been an inspiration to all Americans."
American terror, page 13