Federal judge Richard Matsch gave McVeigh a month to change his mind, but as the deadline passed officials began planning for his death by lethal injection. He reserves the right to seek clemency from the president.
The Federal Bureau of Prisons said it had notified McVeigh of the decision.
Last month McVeigh made a plea to be executed, apparently giving up attempts to have a re-trial.
Federal judge Richard Matsch gave McVeigh a month to change his mind, but as the deadline passed officials began planning for his death by lethal injection. He reserves the right to seek clemency from the president.
McVeigh's lawyer, Nathan Chambers, said he had 30 days to file a petition for clemency.
A Gulf War veteran, McVeigh stands to become the first person in America executed under federal, rather than state, jurisdiction in nearly 40 years.
'Fit to die'
McVeigh's 11 December plea to be executed marked a reversal of his attempts, since being sentenced to death in 1997, to have a retrial.
In his death plea, McVeigh argued that he was mentally fit to be executed.
But he gave no explanation as to why he would no longer appeal against his death sentence.
The Oklahoma City bomb attack, on a federal government building in the city, was the worst terrorist attack on US soil, leaving more than 500 injured.
Nineteen children were killed in the bombing.
McVeigh, currently interned in an Indiana federal prison, was found guilty of driving a lorry laden with explosives into the Alfred P Murrah Federal Building on 19 April 1995.
His former army friend Terry Nichols is serving life imprisonment after being found guilty in a separate trial of conspiracy to carry out the bombing.