He is alleged to have killed his brother Rudi and parents Martin and Teresa, and left his sister Marli struggling with near-fatal injuries.
The trial, which opened in Cape Town after several delays, has attracted international interest as police failed to arrest anyone for the grisly killings until Henri van Breda handed himself in to police.
Van Breda is alleged to have killed his brother Rudi and parents Martin and Teresa, and left his sister Marli struggling with near-fatal injuries to her head, neck and throat.
The events took place on January 27, 2015 at the family's luxury home at an exclusive golf estate in Stellenbosch outside Cape Town, where they lived after returning from several years in Australia.
At the Western Cape High Court, van Breda, dressed in a suit and tie, quietly said "not guilty" to three counts of murder and one of attempted murder.
In a statement read out by his lawyer Pieter Botha, van Breda said that a masked intruder had entered the house and attacked his family with an axe in the early hours of the morning.
The accused said he could "make out the silhouette of somebody" attacking his brother in the high-security property.
"I shouted for help, shouting to attract attention," he said.
Van Breda said his father came into the room "trying to tackle the attacker."
"My father was struck as he lunged towards the attacker. He was hit a number of times... I also recall the attacker was laughing."
Van Breda said he heard his mother's voice, and then the attacker left the room.
According to media reports, Rudi, a 21-year-old engineering student, was found on a blood-soaked bed next to his father, 54.
Both were killed by savage blows from the axe.
His mother, 55, was found with a gaping head wound on the bedroom's balcony.
Marli, then 16, was left in a coma after the attack and suffered memory loss, but she may give evidence during the trial.
Van Breda himself had only minor bruises and scratches, which experts say may have been self-inflicted.
On Monday, he said in his statement that he had passed out after disarming the attacker, who then fled the house.
"I later woke lying on the stairs. I was unsure how long I was unconscious... I could see it was light. I then saw Marli moving. I could also hear what sounded like Rudi making gurgling sounds," he said.
In a leaked tape of his call to emergency services, van Breda said his family members were "bleeding from the head" before he appeared to giggle briefly.
Van Breda in his statement said he was in the toilet playing games on his phone when the intruder broke in.
He described his family as "fairly close-knit" who enjoyed boating and shark cage diving together.
Before the attack, they had spent the evening watching a Star Wars movie, while their mother spoke on the phone.
The run-up to the trial generated fevered interest over a privileged son allegedly unleashing a savage attack on his family, whose fortune has been estimated at $16 million.
There is a continuing legal battle over whether the trial can be broadcast live on television.
Local reports suggested van Breda had spent time in drug rehabilitation before the deaths. He was enrolled as a science undergraduate at the time.
He handed himself in to a local police station 18 months after the attack, during which time the police had made no arrests.
Since being arrested, he has been on $8,000 bail while living with his girlfriend.
The trial continued Monday.