Anni’s family, including her father Vinod Hindocha and mother Nilam, were among those taking their seats in the packed courtroom on Monday.
Mr Hindocha, 65, had described the four-year wait for justice into her murder as “torture”.
He said: “Since that terrible day it has been a period of torture and we have missed her each and every minute of each and every day.”
A German rent boy Leopold Leisser is expected to be a key witness, who will tell the court Shrien Dewani paid him for sex in the months leading up to the shooting and told him he regretted his engagement to Anni, but was too ashamed to back out.
Mr Hindocha said: “Now that I am back here all I ask for is the full story and justice.
“I am confident that South Africa will conduct a fair and open trial of Shrien Dewani.”
Dewani was extradited to Cape Town in April after losing a three-year UK court battle in which he claimed he was mentally unfit to stand trial.
After his wife’s death, he told South African police the couple were carjacked at gunpoint as they took a taxi outside the city to the Gugulethu township where Anni “wanted to see the real Africa”.
He claimed he and the driver were thrown out of the vehicle before two abductors kidnapped his new wife.
Her body was found in the back of the abandoned taxi the next morning.
But the driver Zola Tongo said Dewani had offered him £1,300 to arrange for his wife to be killed.
Tongo and two other local men, Xolile Mngeni and Mziwamadoda Qwabe, are already serving long jail sentences for Anni’s murder.
Anni’s cousin Sneha is likely to be another witness, and is expected to tell the court that Anni wanted to stop her wedding, a lavish affair in Mumbai.
Anni, who was born in Sweden, met Shrien after moving to London to stay with Sneha.
As Anni’s family were preparing to leave Sweden to attend the trial, her elder sister Ami, 37, told Sky News last week: “Three weeks before the wedding Anni actually threw the ring back at Shrien. She called me and said a lot of things like it wasn’t working well.
“I thought she was just stressed out and told her she would get over it.
“Looking back, I should have told her to break it off. If I had, maybe she would be alive today.
“It still haunts me.”
Unlike the murder trial of athlete Oscar Pistorius in Pretoria this year, Dewani’s trial will not be televised, though cameras may be allowed in briefly to film him in the dock.
The hearing is expected to last until mid-December.