Steven Hastings Barker, 74, is accused of murdering his wife Christine Barker at their Bronte home on Thursday night.
Ms Barker, also 74, was found by police with critical injuries outside the home on Bronte Road about 6pm.
Police and paramedics treated her, but she died a short time later in hospital.
Her husband was arrested at the scene and taken to Waverley Police Station, where he was charged with murder.
The property in the beachside suburb remained cordoned off the morning after the death, with numerous detectives and uniformed officers at the scene.
Barker was refused bail by a Waverley magistrate on Friday after police prosecutor Sergeant Nicole McMahon said the evidence against the accused murderer was overwhelming.
As forensic and crime scene evidence was analysed, the case against him was only likely to strengthen, she said.
If convicted, the engineer faces life in prison.
Barker's admissions to killing his wife were captured on the body-worn cameras of officers who arrived at the home, Sgt McMahon said.
The alleged murder occurred in front of a child who had been inside the home, she said.
Defence lawyer Matthew Bogunovich said his client was not an unacceptable risk to the community or fleeing the state.
Barker had no criminal record, a long employment history and had only been overseas three times despite his considerable means, the court was told.
Thursday's alleged murder occurred after an unravelling in the Barkers' long marriage and the accused killer did not pose a threat to the wider community, Mr Bogunovich said.
Prison would likely be tough for Barker as a first-time offender, but on the balance of the serious charges against him and the strength of evidence against him, there was not enough reason to grant him release, magistrate Clare Farnan said.
Barker dropped his head into his chest as his bail request was denied.
A small group of supporters went to Waverley Local Court on Friday but declined to speak with media.
Barker will appear at the court again on December 7.
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