McVeigh, 32, was convicted in 1997 of the 1995 bombing of an Oklahoma City federal building which killed 168 people, 19 of them children.
McVeigh, 32, was convicted in 1997 of the 1995 bombing of an Oklahoma City federal building which killed 168 people, 19 of them children.
His execution by lethal injection is due to take place on 16 May in Terre Haute, Indiana, and will be the first carried out by the US federal authorities since 1963.
Several US states have previously allowed the relatives of murder victims to witness executions on CCTV.
On hearing the news, Jannie Coverdale, whose two grandsons died in the blast, said: "This is something I've wanted to watch."
'Special provisions'
Mr Ashcroft's decision provides for the execution to be beamed via a video link to an unnamed location in Oklahoma City.
Federal prison regulations prohibit public broadcasts of executions, but the US prisons bureau had been considering CCTV in order to accommodate the large number of relatives and survivors who want to watch McVeigh's last moments.
"The Oklahoma City survivors may be the largest group of crime victims in our history," Mr Ashcroft said.
"The Department of Justice must make special provisions to assist the needs of the survivors and the victims' families."
He said McVeigh would be able to use the 15 minutes a day of phone calls to which he is entitled to talk to reporters, but urged the media to exercise restraint, explaining that he wanted to restrict "a mass murderer's access to a public podium".
TV request denied
Officials have rejected McVeigh's request that the execution be broadcast live on national television.
Mr Ashcroft said the transmission would begin at the same time the curtain is opened for witnesses at the prison and that viewers would be able to see McVeigh on the execution table and hear any last statement he might make.
He said there would be no recording of the execution and the FBI would put in place stringent security to make sure nobody could record or pirate the CCTV feed.
Two internet companies are appealing against a decision not to grant them rights to broadcast the execution, saying it is an infringement of their freedom of speech.
Mr Ashcroft also said the number of victim witnesses in the prison execution room would be increased to 10, with an equal number of seats reserved for the media.