According to a report in the Daily Mirror, Xolile Mngeni told prison bosses the 28-year-old newly-wed was executed as she cowered in the back of the cab he had snatched.
And Mngeni alleged 30-year-old care home boss Shrien opened the door of the taxi and walked away before his wife was shot dead and he was not thrown out of the window as he claims, the report said.
23-year-old Mngeni was speaking about the last moments of Anni's life from a prison near Cape Town where he is awaiting trial for murder and kidnap.
His claims contradict those that Anni and her husband Shrien were the victims of a botched robbery while on honeymoon in South Africa.
A jail source said: "The purpose of the exercise was simply to kill. Rape was never part of the plan."
Butt Mngeni, 23, stopped short of implicating Shrien – fighting extradition to South Africa where he faces charges over his wife's death – claiming he did not know who ordered Anni's death. He has not revealed whether he or co-accused Mziwamadoda Qwabe, 25, pulled the trigger.
The jail source added: "He has admitted he was at the heart of it. He says he was told by Qwabe that there was somebody he needed to kill and he would be paid."
Mngeni and Qwabe travelled together to an arranged ambush point in the township of Gugulethu where Anni and Shrien arrived in a taxi driven by Zola Tongo.
The 31-year-old cabbie, jailed for 18 years for his part in the murder, claims Shrien paid the gang 1,400 pounds to have his wife killed.The Bristol businessman has strenuously denied any involvement in Anni's death, describing the claims as "ludicrous".
His lawyer, Clare Montgomery claimed a group of robbers and murderers were desperate to escape a life sentence by falsely accusing him.
Shrien's representative Max Clifford also rejected Mngeni's claims after the accused alleged he was tortured during interrogation. He said: "If this man was tortured, then you cannot rely too much.