The decision could leave Pistorius open to a prison sentence of at least 15 years if he is convicted of murder.
"I cannot say the prospect of success at the Supreme Court is remote," Judge Thokozile Masipa said in granting the appeal.
The Olympic and Paralympic track star, aged 28, is currently serving prison time after being convicted in October of culpable homicide after a seven-month trial.
He has admitted killing Steenkamp on Feb.14, 2013, by firing four shots into the locked door of a toilet cubicle in what he said was the mistaken belief an intruder was hiding behind it.
Masipa said during sentencing that the state failed to convince her of Pistorius' intent to kill when he fired.
But state prosecutor Gerrie Nel said in his application to appeal that the judgement was "shockingly inappropriate" and argued that even if Pistorius did not know Steenkamp was behind the door when he fired, he showed intent to kill whoever was there.
In granting the application, Masipa said the prosecution's points were questions of law and should therefore go to the Supreme Court of Appeal for consideration.
South Africa's National Prosecuting Authority (NPA) welcomed the decision.
"Our argument was that he should have been convicted of murder. That is, of course, what we would like to happen," NPA spokesman Nathi Mncube said.
The NPA was criticised over the original conviction against Pistorius and faced further disdain this week for bungling the murder case against British national Shrien Dewani, who was cleared on Monday of conspiring to kill his wife during their honeymoon in Cape Town.
The matter that will be heard next year will evaluate if Masipa's ruling based on the legal principle of 'dolus eventualis' was correctly applied and if prosecutors succeed, they can demand a stiffer sentence.
Masipa's original decision to rule out murder was criticised by several legal experts and the Women's League of the ruling African National Congress (ANC) as an erroneous interpretation of the law.
By the time the appeal is heard before a panel of South Africa's most senior judges, Pistorius, who did not attend the appeal process, could be out of prison as his five-year sentence only requires that he serves 10 months behind bars and the balance under house arrest.
Pistorius, whose lower legs were amputated as a baby, became one of the world's most celebrated athletes after he became a Paralympic champion then took part in the 2012 Olympics and other international events.
The killing of Steenkamp, a 29-year-old model and law graduate, led to one of the most sensational trials in South Africa's recent history and cost him his reputation and his fortune.
(Reporting by Peroshni Govender, Editing by Angus MacSwan)
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