Sentencing is up to the North Gauteng High Court, where Pistorius was tried. South African media said Judge Thokozile Masipa, who presided over the original trial, will handle the matter. No sentencing date has been set.
The National Prosecuting Authority will wait for word from the trial court about possible sentencing dates, said Luvuyo Mfaku, a spokesman for the authority.
The Pistorius family said in a statement: "The legal team will study the finding and we will be guided by them in terms of options going forward."
Johann Engelbrecht, a criminal lawyer who is not involved in the Pistorius case, said it is doubtful that the former athlete's lawyers could challenge the murder conviction by appealing to the Constitutional Court. He speculated that prosecutors would want the sentencing process to proceed swiftly rather than let Pistorius remain under house arrest for an extended period.
Pistorius, a multiple Paralympic champion, became the first amputee to run at the Olympics and the able-bodied world championships. He was known as "Blade Runner" for his carbon-fibre running blades.
"This case involves a human tragedy of Shakespearean proportions," Leach said while delivering the ruling on behalf of the five-judge appeals court.
"A young man overcomes huge physical disabilities to reach Olympian heights as an athlete," he said. "In doing so he becomes an international celebrity. He meets a young woman of great natural beauty and a successful model. Romance blossoms and then ironically, on Valentine's Day, all is destroyed when he takes her life."
Steenkamp, a model who appeared in a television reality show, had planned to give a speech touching on domestic abuse and family relationships at a school on the day she died. In a tweet the day before she died, she wrote: "What do you have up your sleeve for your love tomorrow???"
Leach witheringly described Pistorius' often tearful trial testimony as "vacillating and untruthful" and said Masipa, the judge who convicted him of manslaughter, committed an "error in law" by incorrectly applying a legal principle called "dolus eventualis".
Under that concept, a person can be convicted of murder if he or she foresaw the possibility of someone dying through their actions and went ahead anyway.
Pistorius, 29, insisted he shot Steenkamp by mistake, thinking there was an intruder behind the door of a toilet cubicle in his home. The prosecution said Pistorius shot Steenkamp during an argument.
Leach said that regardless of who Pistorius said he thought was behind the door, he should have known someone could be killed if he fired.
There was initial confusion in the court when the judge preceded his reading of the Pistorius ruling by saying an appeal had been dismissed. He was referring to a separate legal case, but some news organisations incorrectly reported that Pistorius had not been convicted of murder. The Associated Press did not make the error. It was unknown if Pistorius was watching the TV broadcast or monitoring the initial news reports online that suggested he would serve no more prison time.
There was no sign of Pistorius outside the home of his uncle, Arnold. As the judge began to read the decision, broadcast live on TV, the uncle was seen rushing into the house. Later, the uncle drove off in a car.
Reeva Steenkamp's father, Barry, told South African television channel ANN7 that the judgment was fair.
"Let us now all get on with our lives," he said. His voice breaking with emotion, he said of his daughter: "I'm sure she'll be able to rest as well now."
-AP
