The State had appealed to the court against the leniency of the initial six-year jail sentence.
Pistorius was once best known for winning gold at the 2004 Athens Paralympics and for successfully fighting to compete in the 2012 London Olympics alongside able-bodied runners.
Johnson said the High Court did not list the substantial and compelling factors for deviating from the 15-year sentence and that Pistorius had not shown remorse for the murder.
Pistorius killed Steenkamp in the pre-dawn hours of Valentine's Day 2013 after shooting four times through a closed toilet cubicle door with his 9 mm pistol.
"They feel there has been justice for Reeva". He pleaded not guilty at his trial in 2014 and has always denied that he killed Steenkamp in a rage, saying he mistook her for a burglar.
However, the former athlete's case has been brought back to the South African Supreme Court of Appeal, where that sentence has been upgraded to 13 years and five months.
The NPA said the six-year sentenced was shockingly low and if they had allowed it to stand, it would have set a bad precedent.
The ruling added that Pistorius "displays a lack of remorse and does not appreciate the gravity of his actions".
The court said Pistorius should have been sentenced to 15 years, but the judges accounted for the time already served by the former track star.
The new sentence was backdated to start on the day he began his murder sentence, on July 6 previous year.
He was sentenced to six years.
"I did not expect the Supreme Court of Appeal to hand down such a lengthy sentence of imprisonment", legal analyst Ulrich Roux said on the eNCA news channel.
At the same time, Steenkamp's parents have sent their love to Jayde Panayiatou's parents after her husband, Chris, was sentenced to life in prison for her murder.
Oscar Pistorius sits in the dock during his sentencing hearing at North Gauteng High Court on June 13, 2016 in Pretoria.
Pistorius can appeal the new sentence, according to Kelly Phelps, an adviser to his defense team, but no decision has been made.
Pistorius failed with an appeal to the Constitutional Court a year ago to challenge his murder conviction.