(CNN) Oscar Pistorius has been found guilty of the murder of Reeva Steenkamp after South Africa's Supreme Court of Appeal overturned the previous conviction of culpable homicide.

Judge Eric Leach ruled Thursday that the Paralympic gold medalist should have foreseen that his firing of a gun would have killed whoever was behind the door in his bathroom, regardless of whether he thought it was Steenkamp or an intruder.

State prosecutors appealed the verdict of culpable homicide, seeking a conviction on more severe charges.

The original court judgment had been "fundamentally flawed," Leach said.

Pistorius shot girlfriend Reeva Steenkamp, a model, four times through a locked toilet door on Valentine's Day 2013, saying he mistook her for an intruder.

His jail term hasn't been decided, but he faces up to 15 years in prison.

In October, Pistorius was allowed to move from prison, where he served a year of his original five-year sentence, to house detention.

Steenkamp's family members were present for Thursday's proceedings, remaining stony-faced throughout but hugging after hearing the verdict.

'Tragedy of Shakespearean proportions'

The judge called the circumstances surrounding Steenkamp's death "a human tragedy of Shakespearean proportions."

The ruling rested over the concept of dolus eventualis, or whether Pistorius should have foreseen his actions would lead to death.

Photos: 'Blade Runner' Oscar Pistorius Photos: 'Blade Runner' Oscar Pistorius South African sprinter Oscar Pistorius shakes hands as he leaves a courtroom in Pretoria, South Africa, on Wednesday, July 6. Pistorius, the first double-amputee runner to compete in the Olympics, was sentenced to six years in prison after he was found guilty of murdering his girlfriend, model Reeva Steenkamp, in February 2013. Hide Caption 1 of 19 Photos: 'Blade Runner' Oscar Pistorius Pistorius walks without his prosthetic legs during his sentencing hearing in Pretoria on Wednesday, June 15. His attorney was arguing that he was a vulnerable figure who should receive a lesser sentence for murder. Hide Caption 2 of 19 Photos: 'Blade Runner' Oscar Pistorius Pistorius arrives outside a courtroom in Pretoria in October 2014. He was initially convicted of culpable homicide and sentenced to five years in prison, but a higher court reversed it to murder after an appeal. Hide Caption 3 of 19 Photos: 'Blade Runner' Oscar Pistorius A picture taken on January 26, 2013, shows Pistorius and Steenkamp at Melrose Arch in Johannesburg. Pistorius said her shooting death was an accident after he mistook her for an intruder. The prosecution called it a deliberate act after the two had an argument. Hide Caption 4 of 19 Photos: 'Blade Runner' Oscar Pistorius Pistorius puts his head in his hands during his trial in South Africa in March 2014. Pistorius often showed great emotion as the court went into detail about Steenkamp's death. Hide Caption 5 of 19 Photos: 'Blade Runner' Oscar Pistorius Pistorius leaves a police station with his face covered in February 2013. Hide Caption 6 of 19 Photos: 'Blade Runner' Oscar Pistorius Pistorius won gold for the first time at the 2004 Athens Paralympics. He won the 200-meter final and set a new world record. The South African sprinter was called the "Blade Runner" because of his carbon-fiber prosthetic legs. Hide Caption 7 of 19 Photos: 'Blade Runner' Oscar Pistorius Prosthetic legs stand on the ground as Pistorius coaches children in Manchester, England, in April 2006. Hide Caption 8 of 19 Photos: 'Blade Runner' Oscar Pistorius Pistorius competes in a 400-meter race in Berlin in June 2008. Hide Caption 9 of 19 Photos: 'Blade Runner' Oscar Pistorius Pistorius is seen in Rome during a race in July 2008. Hide Caption 10 of 19 Photos: 'Blade Runner' Oscar Pistorius Pistorius wins gold ahead of Americans Jerome Singleton, left, and Marlon Shirley, right, in the 100-meter T44 during the 2008 Beijing Paralympic Games. Hide Caption 11 of 19 Photos: 'Blade Runner' Oscar Pistorius Pistorius poses with his medals from the IPC Athletics World Championships in January 2011. He won three world titles there but lost the 100-meter T44 final to Singleton. It was his first loss in a race over 100 meters since the 2004 Paralympic Games. Hide Caption 12 of 19 Photos: 'Blade Runner' Oscar Pistorius Pistorius passes the baton to Ofentse Mogawane in a 4x400-meter relay race during the IAAF World Athletics Championships in Daegu, South Korea, in September 2011. Pistorius was the first double-amputee athlete to compete at the World Athletics Championships. Hide Caption 13 of 19 Photos: 'Blade Runner' Oscar Pistorius Pistorius races in the men's 400 meters during the 2012 Olympic Games in London. Hide Caption 14 of 19 Photos: 'Blade Runner' Oscar Pistorius Pistorius competes in the London Olympics. Hide Caption 15 of 19 Photos: 'Blade Runner' Oscar Pistorius Pistorius carries the South African flag during the opening ceremony of the 2012 Paralympics in London. Hide Caption 16 of 19 Photos: 'Blade Runner' Oscar Pistorius Pistorius competes in a men's 400-meter T44 heat at the 2012 Paralympic Games. Hide Caption 17 of 19 Photos: 'Blade Runner' Oscar Pistorius Pistorius poses on the podium with his gold medal after winning the men's 400-meter T44 final at the 2012 Paralympic Games. Hide Caption 18 of 19 Photos: 'Blade Runner' Oscar Pistorius Pistorius receives his honorary doctorate from Strathclyde University in Glasgow, Scotland, in November 2012. Hide Caption 19 of 19

Leach slammed the original judge's failure to assess adequately ballistic evidence that showed Pistorius' firing in to the bathroom stall would have resulted in the person inside being struck.

It was "common sense" that Pistorius must have known he was carrying out a potentially lethal act that "gambled with life" when he fired his gun through the closed toilet door, he said.

"All the shots fired through the door would almost inevitably have struck the person behind it. There would be effectively no place to hide," Leach said.

He called Pistorius' testimony about his actions "unacceptable," "vacillating" and "contradictory."

Photos: Steenkamp: Law student to cover girl Photos: Steenkamp: Law student to cover girl Steenkamp: From law student to cover girl – South African model Reeva Steenkamp died in February 2013 after she was shot at the home of her boyfriend, Olympic sprinter Oscar Pistorius. She was 29. Pistorius has been found guilty of the murder, after South Africa's Supreme Court overturned the previous conviction of culpable homicide. Hide Caption 1 of 8 Photos: Steenkamp: Law student to cover girl Reeva Steenkamp: From law student to cover girl – Before she started dating Pistorius, Steenkamp was famous in her own right. She was a law school graduate with a vibrant personality and several modeling contracts under her belt. Hide Caption 2 of 8 Photos: Steenkamp: Law student to cover girl Steenkamp: From law student to cover girl – A 21-year-old Steenkamp poses on a beach in Port Elizabeth, South Africa, where she grew up. Steenkamp's friend Kerry Smith photographed the aspiring model when she was a law student. Hide Caption 3 of 8 Photos: Steenkamp: Law student to cover girl Steenkamp: From law student to cover girl – Steenkamp poses for another photo taken by Smith. Steenkamp was born in Cape Town, but she moved to Johannesburg to pursue modeling. Hide Caption 4 of 8 Photos: Steenkamp: Law student to cover girl Steenkamp: From law student to cover girl – Pistorius admitted to shooting Steenkamp, but he said it was an accident. Hide Caption 5 of 8 Photos: Steenkamp: Law student to cover girl Steenkamp: From law student to cover girl – Steenkamp appeared as a contestant on a South African reality show, "Tropika Island of Treasure." Her pre-recorded episode aired two days after her death. Hide Caption 6 of 8 Photos: Steenkamp: Law student to cover girl Steenkamp: From law student to cover girl – Steenkamp served as a presenter for FashionTV in South Africa. She was also an FHM cover girl and the face of cosmetics company Avon. Hide Caption 7 of 8 Photos: Steenkamp: Law student to cover girl Steenkamp: From law student to cover girl – Steenkamp "was the kindest, sweetest human being; an angel on Earth," said Capacity Relations, the agency that represented her. Hide Caption 8 of 8

Prosecutors had argued that the 29-year old -- known as the "Blade Runner" in a reference to the prosthetic legs he uses when he races -- intentionally killed Steenkamp following an argument.

Leach said that although Pistorius had genuine beliefs his life was in danger, he should have acted more rationally.

He never fired a warning shot and shot not once but four times.

"The identity of victim is irrelevant to his guilt," he said.

Double jeopardy?

CNN legal analyst Kelly Phelps said that double jeopardy -- a defense that prevents a criminal defendant from being retried on the same charges following a verdict -- did not technically apply in the Pistorius case for two reasons.

The first was that Pistorius wasn't completely acquitted on the original charge but had been convicted of culpable homicide.

JUST WATCHED The Oscar Pistorius trial in 90 seconds Replay More Videos ... MUST WATCH The Oscar Pistorius trial in 90 seconds 01:30

"Strictly speaking, because murder wasn't a separate charge but was tied in with the culpable homicide charge, it's not considered technically ... as reconsidering a case where there has been a complete acquittal," said Phelps, a senior lecturer in law at the University of Cape Town.

The second reason, she said, was that the appeal "was based on a question of law, not a question of fact."

"The argument is that where there's been a mistake in law that's been made -- that is the only reason that an incorrect verdict has been reached -- it would be offensive to the interests of justice in order to allow that verdict to stand," she said.

Final avenue of appeal

Phelps said Pistorius had one final avenue of appeal remaining -- to take the case to the country's Constitutional Court.

A spokesman for Pistorius's camp said his defense is considering his legal options.

Phelps said she believed it was "quite likely" that Pistorius would take his appeal to that court, and she "wouldn't be surprised" if the question of double jeopardy was something his legal team explored in their appeal.

JUST WATCHED A rare look inside Oscar Pistorius' jail cell Replay More Videos ... MUST WATCH A rare look inside Oscar Pistorius' jail cell 01:42

"The issue of double jeopardy hasn't really been robustly debated in this particular context since the advent of our constitution, and I do think there are grounds for debate on reappraising the current approach," she said.

"I certainly don't think that it is the end of the story. This simply marks the end of one phase and the beginning of another one."

Pistorius has been under house arrest at his uncle's residence since being released from prison in October after serving a year.

South Africa's National Prosecuting Authority has said he can remain there until sentencing occurs on his new conviction, most likely next year.

Leach said the courts would take into account time already served in the sentencing.