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Judge Thokozile Masipa, issuing the ruling in court in Pretoria, also gave Pistorius a three-year suspended sentence for a firearms charge. Pistorius has been taken to the cells.
The prosecution had called for a minimum 10-year sentence; the defence for community service and house arrest.
Pistorius was convicted of culpable homicide but cleared of murder.
Judge Masipa began reading the sentence by saying that, although she had been aided by assessors, the decision was hers and hers alone.
She said: “Sentencing is about achieving the right balance. Sentencing is not a perfect exercise.”
She said there must be a balance between retribution, deterrence and rehabilitation.
The judge then summarised the evidence brought before the trial.
She described the evidence of defence witness and social worker Annette Vergeer as “slapdash and disappointing”.
Vergeer had argued Pistorius would be “a lot more vulnerable than the normal man” in jail.
But Judge Masipa said she was sure prisons were equipped to cater for the requirements of a special needs inmate.
She also said she had a “feeling of unease” at what she called an overemphasis on the athlete’s vulnerability.
However, she said Pistorius had made an “enormous contribution to society”, in his charity work and in changing the public perception of disability.
The judge then read out a quote from previous legal opinion, saying that if sentences were too lenient, the administration of justice may fall into disrepute.
She said she found the suggestions of sentences made by defence witnesses “not appropriate”.
Pistorius, 27, an amputee sprinter who became the first athlete to compete in the Olympic and Paralympic Games, killed Steenkamp on Valentine’s Day last year.
He says he shot her by mistake, fearing there was an intruder in his house in the capital, Pretoria.
Steenkamp, a 29-year-old model, reality TV star and law graduate, was hit three times by bullets fired by Pistorius through a toilet door.
Last month, Judge Masipa cleared Pistorius of murder, but convicted him of culpable homicide, saying he had been negligent.
The high-profile, seven-month trial has captured public attention in South Africa and beyond.
There was no legal limit on the length of a jail term, but experts say the typical maximum sentence for culpable homicide is around 15 years.
However, despite the sentencing being announced, the case may not be over.
Both the prosecution and the defence have the right to appeal against the sentence.