Sex offender Christopher Hector, who was serving a 20-year sentence, had previously refused to shield when there was an outbreak of the deadly illness in HMP Wakefield, a report found.
The 62-year-old died from respiratory failure caused by coronavirus-related pneumonia in December last year.
He is one of six prisoners at the maximum security Love Lane prison to have contracted Covid-19 and died so far.
Hector had been serving at HMP Leeds at the start of the pandemic, and due to his obesity and mild asthma was advised to shield, which he refused.
In June last year, he "had a change of heart" and began shielding before being transferred to HMP Wakefield in September where he spent two weeks in mandatory isolation on arrival.
This was in conjunction with the prison rules to help prevent the transfer of Covid-19 from incoming prisoners.
He was then moved into a single cell, and following the outbreak in the prison he began developing breathing problems in December, he was taken to hospital where he tested positive.
He refused a ventilator and died on December 23.
The report concluded: "The clinical reviewer concluded that the clinical care Mr Hector received at Wakefield was equivalent to that which he could have expected to receive in the community."
Hector was jailed in March last year for historic rapes of a young girl dating back more than 30 years, which he denied but was found guilty of after a week-long trial.