He was satisfied the law ensured a 'proper balance between the principle of open justice on the one hand, and on the other the need to ensure victims of sexual offences are encouraged to come forward'.
Mr Howard's decision followed his review of the issue of anonymity after concern over the case of Austen Donnellan, the student at King's College, London, cleared last October of raping a student who claimed he violated her as she lay drunk and unconscious after a Christmas party.
Mr Howard said he was not persuaded that defendants in cases involving sexual offences should be treated differently from those charged with other serious crimes who feared their reputation would be damaged.
'In a system of open justice, some discomfort for defendants who are subsequently acquitted is inevitable,' he said.
'But openness is essential to the maintenance of public confidence in the criminal justice system and ensures that information that might encourage further witnesses to come forward is publicly available.
'I do not consider there is a special case for infringing that principle in relation to defendants in sexual offence cases either as a matter of general application or of judicial discretion in the individual case.'
He maintained the identity of victims must be protected.
'Even with anonymity, a criminal trial is a particularly harrowing process for the victim of a sexual offence and I believe that any diminution in the protection currently available, or doubts about the certainty of the protection, would be likely to increase the number of sexual offences that go unreported and unpunished.
'The law already allows for the prosecution of complainants whose accusations amount to perjury or an attempt to pervert the course of justice, and in those circumstances the rules relating to anonymity no longer apply.'
Anonymity for victims was introduced under the 1976 Sexual Offences (Amendment) Act, which also gave protection to defendants from the moment they were accused of rape until conviction. But growing disquiet over the anonymity rule for defendants led to its abolition in the 1988 Criminal Justice Act.
The 1988 Act also closed a loophole that had meant victims' anonymity only came into force when a person was accused of the rape. The gap was highlighted in the Ealing Vicarage rape case when the rape victim was identified while police were tracking down her assailants.
The 1992 Sexual Offences (Amendment) Act extended protection to other victims of sexual offences.
Jennifer Temkin, professor of law at Sussex University and author of Rape and the Legal Process, welcomed the Home Secretary's decision. Altering the balance would have 'put the clock back on rape'.
Professor Temkin said that after the Donnellan case there were suggestions that women should be named if the defendant was acquitted. But that would have been 'a terrible deterrent to women to come forward'.
She said it would also have been difficult to justify singling out one group of defendants for protection.