The Back to Black star was found dead at her north London home last year, aged 27.
Greenaway recorded a verdict of misadventure at the original hearing last year.
She was appointed to the role in July 2009 by her husband, Andrew Reid, who was the coroner for Inner North London, after she had worked as a solicitor and barrister in Australia.
But she stepped down in November when it emerged she did not have the requisite five years' experience in the Law Society.
Reid resigned from his position this month after the Office for Judicial Complaints (OJC) launched disciplinary proceedings against him.
Investigators found he had not "thoroughly" checked his wife had the requisite qualifications for the position.
The Lord Chancellor and the Lord Chief Justice had indicated their intention to remove Reid from judicial office following the investigation.
But despite being entitled to challenge their decision, the senior coroner decided to stand down.
During her time as deputy assistant coroner, Greenaway conducted 12 inquests in Camden, but worked largely from Poplar Coroner's Court in east London.
According to British law, Greenaway, who also worked as a nurse in Australia, would have needed either five years with the Law Society or five years of experience as a qualified medical practitioner.
She met neither set criteria.
The new inquest will be at St Pancras Coroner's Court on Tuesday, January 8.
A spokesman for the Winehouse family said: "The family were happy with the way the original inquest was conducted and did not request it to be reheard.
"This seems to be a matter of procedure and the verdict is not expected to change."