The 74-year-old life prisoner, dubbed the Yorkshire Ripper, had been suffering increased breathlessness and needed additional oxygen in the days before his death in November.
Sutcliffe murdered 13 women and attacked more, terrifying northern England in the late 1970s until he was caught in 1980.
He had been serving a life sentence at Frankland Prison, Durham, and was transferred to the nearby University Hospital of North Durham on November 10.
The assistant senior coroner for County Durham, Crispin Oliver, held a 15-minute hearing in Crook to hear an update on investigations ahead of a full hearing later this year.
Mr Oliver read an extract from the post-mortem examination by Dr Clive Bloxham, carried out at the Freeman Hospital, Newcastle, days after Sutcliffe died.
The serial killer tested positive for coronavirus on November 5.
The prisoner, who changed his name by deed poll to Coonan in 2001, had previously suffered from diabetes and heart disease, known risk factors for Covid-19, the coroner said.
He had a pacemaker fitted on November 2 and there were no complications. Referring to the post-mortem, Mr Oliver said: "However, he continued to deteriorate with increasing oxygen requirements and on November 12 he was judged to be dying.
"After full discussion with the patient, he was transferred to palliative care and he died on November 13 at 1.45am."
The coroner said the post-mortem confirmed severe heart disease, including stenosis of three coronary arteries.
He added: "The main finding was very heavy, solid and airless lungs, highly typical of adult respiratory distress syndrome, this is a characteristic feature of individuals dying of Covid-19 infection."
Sutcliffe's next-of-kin, ex-wife Sonia Woodward, had been in contact with the coroner's service but did not attend the hearing.
Mr Oliver is awaiting a report by the Prisons and Probation Ombudsman into Sutcliffe's death, with its initial findings due on April 8.
A full inquest was provisionally scheduled for May 7, but that could become a pre-inquest review if the ombudsman's report reveals more issues to consider.
If needed, a full inquest would then happen on June 18, the coroner said.
Reporting by PA