Barry George is serving a life sentence
Barry George, 41, of Fulham, West London, was sentenced to life imprisonment on 2 July this year.
Three senior judges, who will scrutinise the case, have the power to overturn the guilty verdict, order a retrial or keep the 41-year-old in jail.
The Crown Prosecution Service told BBC News Online that George had been given leave to appeal against his conviction.
BBC crime correspondent Stephen Cape said the appeal was granted on a number of grounds including identification evidence and possible contamination of evidence.
He said the case was expected to be heard next summer.
Evidence questioned
An Old Bailey jury found George guilty of murdering the 37-year-old celebrity on the doorstep of her home in Gowan Avenue, Fulham, in April 1999.
The prosecution claimed a speck of firearms residue was found in an inside pocket of a jacket belonging to George.
Since his arrest, George has maintained claims that he is innocent of the killing.
During his trial, George's legal team argued that the evidence of a number of witnesses who picked him out at identity parades was unreliable.
They also claimed the speck of gunpowder found in George's jacket could have got there through contamination.
His lawyer, Marilyn Etienne, issued a statement within days of his conviction saying that he would lodge an appeal.
George told
She said the prosecution case had rested "primarily and fundamentally" upon identification evidence.
"The judge directed the jury in terms that they could not convict unless they accepted the identification evidence as reliable," she said.
"There was no other evidence which could found a conviction."
A single judge has spent weeks going through the papers before concluding there were grounds to grant George leave to appeal against his conviction, it is reported.
It is understood George was informed about his appeal in prison on Thursday.