"We have taken the decision to appeal both the verdict and the sentence," said a statement from the prosecution, noting that they will publish the details of the appeal "within days".
Pistorius killed Steenkamp Feb 14, 2013, by shooting through a closed bathroom door in their Pretoria residence. He later claimed that he believed he was firing at an intruder who had broken into the house.
While delivering her verdict in Pretoria's High Court, Judge Thokozile Masipa said the athlete, who lost both legs in his early childhood, would be able to receive adequate care in South African prisons.
She then denied the defence's request for a sentence of house arrest and community work.
The prosecution, however, said that Pistorius, on the night of the shooting, had dealt with gross negligence towards the perceived threat of home intruders.
In her Sep 12 verdict, Judge Masipa ruled out convicting Pistorius of murder. She gave credence to Pistorius's story, in which the athlete claimed he had believed an intruder was in the house on the night of the shooting.
Oscar Pistorius, 27, enjoyed great fame in the 2012 London Olympics, when he became the first sprinter in history with artificial limbs to take part in the Olympic Games.
Pistorius stopped competing after the crime and has since lost all his sponsors.