Venod Skantha was yesterday found guilty of stabbing Miss Rush to death in her bed in February last year.
He was also convicted of four counts of threatening to kill, relating to the prosecution's key witness and his family.
The jury only needed three hours to unanimously find him guilty on all counts.
Skantha was arrested and charged with the crime on 4 February last year. At the time he was working as a junior house doctor at Dunedin Hospital.
His practising certificate was withdrawn by the Medical Council 24 days after his arrest.
Medical Council chief executive Joan Simeon said a professional conduct committee was established to investigate the allegations against Skantha.
"The Medical Council took the allegations very seriously and stopped Dr Skantha from practising as soon as possible," Ms Simeon said.
"The professional conduct committee investigation was placed on hold pending the outcome of the criminal trial. The professional conduct committee will resume its investigation immediately.
"An option available to the professional conduct committee is to file a charge in the Health Practitioners Disciplinary Tribunal. If Dr Skantha is found to have been convicted of an offence which reflects adversely on his fitness to practise, the Health Practitioners Disciplinary Tribunal may cancel Dr Skantha's registration."
She extended the council's deepest sympathies to the family of Miss Rush.
The High Court heard Skantha's motive for killing Miss Rush was to save his job at Dunedin Hospital.
She told him she was serious about going to the police and his employer with claims he was "touching up" minors without consent, supplying them alcohol and offering money for sex.
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On 2 February, 2018, the pair shared a terse back-and-forth via a messenger service on social media with Miss Rush ending the exchange with "you know what you were doing when you did it. For that you deserve everything you're gonna get".
Half an hour later she was stabbed to death in her bed.
The court heard how Skantha was already on thin ice at work after showing up in July 2017 while off-duty and after drinking, and treating a patient.
He only saved his job on that occasion by lying about his mother's death.
Skantha will be sentenced for his crimes on March 6.