The Ministry of Justice said the selected low-risk offenders will be electronically tagged and temporarily released on licence in stages, although they can be recalled at the first sign of concern.
It is seen as a way to avoid thousands of prisoners, many of whom share cells, from becoming infected.
The move comes as 88 prisoners and 15 staff have tested positive for Covid-19 so far.
No high-risk criminals - such as those who have been convicted of violent or sexual offences, anyone who is a national security concern or a danger to children - will be considered for release.
Prisoners who have not served at least half their custodial term will also not be released.
The MoJ also said no offender convicted of Covid-19-related offences, including coughing at emergency workers or stealing personal protective equipment, will be eligible.
Lord Chancellor and Justice Secretary Robert Buckland QC said: “This Government is committed to ensuring that justice is served to those who break the law.
“But this is an unprecedented situation because if coronavirus takes hold in our prisons, the NHS could be overwhelmed and more lives put at risk.
“All prisoners will face a tough risk assessment and must comply with strict conditions, including an electronic tag, while they are closely monitored.”
The Prison Officers' Association believes it will relieve the pressure on frontline staff and the crowded prison system which ‘could be the difference between life and death during this pandemic.’
National chairman Mark Fairhurst said: “It is essential that those being released pose no risk to the public and get tested for Covid-19 prior to release. Victims of crime should not be forgotten when such decisions are made and a balance must be struck between the safety of staff and the general public.”
Earlier this week, it was announced that pregnant inmates could be granted temporary release from prison ‘within days’ to protect them and their unborn children.