Pistorius is to be released from jail on 21 August on probation after serving 10 months of his five-year prison term after being found guilty of culpable homicide in the Steenkamp shooting case.
"What I can assure you is that today [17 August] the papers were filed in the Supreme Court of Appeal," said National Prosecuting Authority spokesman Luvuyo Mfaku, reported AFP News.
Pistorius' defense lawyers will have until 17 September to respond and the appeal will be heard by the Supreme Court in November.
If found guilty of murder, the blade runner could face a prison term of at least 15 years.
"[The appeal] will be a fairly dry affair between three or five judges at the supreme court of appeal in Bloemfontein... The main tenet of their appeal is that it doesn't really matter who he [Pistorius] thought was behind that door," reported Sky News.
"They believe he knew that by firing four bullets through that door that he was going to kill someone, and therefore he's guilty of murder."
Pistorius has maintained their was an intruder in his house on the night of the murder.
Meanwhile, Steenkamp's parents released a statement saying: "We are still struggling with coming to terms with losing our precious daughter Reeva and her loss is felt even more this week as we would have celebrated her 32nd birthday on 19 August.
"As a family we want to continue to honour Reeva's memory and will commemorate her birthday by focusing on the Reeva Rebecca Steenkamp Foundation, celebrating her life, what she stood for and the joy she brought into so many lives."