The American student is serving a 26-year prison sentence in Perugia for the brutal killing, which prosecutors said followed a bungled sex game.
Knox's hopes of having the verdict overturned were given a boost by the decision on Saturday although the police case also rests on considerable circumstantial evidence, the lack of alibi, and contradictory statements made by Knox and her boyfriend.
But the court in Perugia also gave permission for defence lawyers to introduce two new witnesses, boosting 23-year-old Knox's chances.
Knox's stepfather, Chris Mellas, described it as "the first step in the right direction".
The 36-year-old said: "We're all pleased. It's nice to have the first good decision in three years.
"Amanda is definitely hopeful. We've always had a little bit of that hope but this is the first time we have a reason for it."
The evidence to be reviewed includes disputed DNA traces found on a knife allegedly used as the murder weapon and on the clasp of Miss Kercher's bra.
Lawyers representing Knox's Italian ex-boyfriend Raffaele Sollecito, sentenced to 25 years for the murder in the same trial last year, also requested a fresh look at this evidence.
Both legal teams have claimed the evidence was inconclusive and also argued it may have been contaminated when analysed.
Prosecutor Giancarlo Costagliola had opposed the request by defence lawyers for a review of the DNA evidence, labelling it "useless". He said: "This court has all the elements to be able to come to a decision."
Lawyer Francesco Maresca, representing the Kercher family, had also been against a review.
Leeds University student Miss Kercher, 21, from Coulsdon, Surrey, was found dead on November 2, 2007, in her bedroom at the Perugia house she shared with Knox and others during her year abroad.
Her throat had been slit and her semi-naked body was partially covered by a duvet.
Rudy Guede, an Ivory Coast man jailed in separate proceedings for the murder and sexual violence, failed to get his conviction overturned last week.