The findings of Coroner Garry Evans are released today after Mr Kahui, who was acquitted in June 2008 of murdering the three-month-old twins, abandoned a legal battle to stop the report being made public.
"The traumatic brain injuries suffered by Chris and Cru Kahui were incurred by them during the afternoon/early evening of 12 June, 2006, whilst they were in the sole custody, care and control of their father," Mr Evans concluded in his report.
The coroner said he was satisfied on the "balance of probabilities", which is the standard of proof required in civil court cases.
In criminal cases, such as the murder trial of Mr Kahui, the standard of proof is the higher "beyond reasonable doubt".
Mr Evans said that if he was wrong about using the balance of probabilities as the standard of proof in this case, he was "satisfied to the point of being sure".
He said an inquest was an inquisitorial hearing to determine facts, not a murder trial.
"The question of how the twins came to meet their deaths is quite different to the question of whether Chris Kahui bears any responsibility in terms of the criminal law for their deaths. He has been found to bear no such responsibility."
Mr Kahui was found not guilty by a jury.
The coroner's conclusion angered Mr Kahui's defence team and supporters.
Barrister Lorraine Smith said her client "objected in the strongest possible terms to the coroner's findings and criticisms of him", which were "inconsistent with his previous acquittal of any involvement in causing the deaths of the twins".
"Mr Kahui also reaffirmed that he denies any involvement in the tragic and untimely deaths of the twins," Mrs Smith said.
Chris and Cru Kahui died in Starship Hospital on June 18, 2006 from head injuries.
Their 21-year-old father was charged with the murders after a four-month police investigation.
Mr Kahui was found not guilty after a seven-week trial at the High Court at Auckland which ended in June 2008.
The jury deliberated for only 10 minutes before delivering its verdict.
The main plank of the defence case was that the twins' mother, Macsyna King, was the killer.
In his findings, Mr Evans said the theory that Ms King was responsible for the deaths was "unsupported by the evidence and is without substance in fact".
She is living in Gisborne and could not be contacted yesterday.
But in a letter she wrote to her former partner, published in the book Breaking Silence by journalist Ian Wishart, Ms King said she could not stop thinking about what happened on the night she left him in charge of the twins.
"I have trouble not blaming myself for ever leaving the boys with you. I tell myself sometimes that this would never have happened if I'd taken them with me or stayed home with them.
"I see their tiny faces if I close my eyes. I remember some of their mouth and hand expressions and I ache to hold them. I shudder when I think of the physical pain their little bodies must have gone through."
Chris Kahui was interviewed three times during the 2006 police investigation but did not give evidence at the 2008 trial.
But he did give evidence during the inquest, and Mr Evans described his testimony as "unreliable, conflicting and, on many occasions, untrue".
"The Court formed a poor view of his credibility," he said.
"Different versions of events have been given by him on different occasions to different people."
