Earlier in the week, the Danish government had asked Rushdie to stay away from the award ceremony on the grounds that the police would not be able to provide for his security.
"I gather there's been a lot of fuss in Denmark today, and a lot of people have been very annoyed about the government's decision. I am delighted that they have so swiftly reversed their decision," Rushdie said.
The Danish culture minister, Jytte Hilten, said in a letter to the author that Denmark "regrets the award ceremony cannot take place as planned, but must assure you that the decision was taken purely on security grounds.
"I would like to invite you and personally present you with your prize in Copenhagen."
Denmark's Prime Minister, Poul Nyrup Rasmussen, said Rushdie would have to scrap his plans to collect the award on 14 November, the date of the ceremony, but would be free to visit Copenhagen "some time before Christmas". He did not specify an exact date.
Rushdie has been living in semi-secrecy ever since the late Iranian spiritual revolutionary leader, the Ayatollah Ruhollah Khomeini, issued a fatwa in 1989 decreeing that he should be killed for his "blasphemous" book, The Satanic Verses. Iran's present rulers say that they are powerless to nullify the fatwa, but stress that they have no intention of sending hitmen to murder the author.
In recent years, Rushdie has travelled widely in Britain and abroad, giving lectures and attending meetings that have sometimes been well-advertised in advance. Earlier this week, he gave a reading of his works in Vienna.
The Danish government had initially said that Mr Rushdie might be in danger in Copenhagen because the police had other urgent matters to deal with, above all the threat of Nordic biker gangs.
One such gang recently fired a rocket-propelled missile into another gang's headquarters in the Danish capital, killing two people.
However, there were immediate protests from human rights groups and politicians in Denmark and abroad.
"I'm disappointed that we sent out a signal which can be interpreted as if we're falling on our knees before the Iranian regime," said Bjoern Elmqvist, a member of the Danish Radical Party.Reuse content