Mr Hancock is seeking someone with experience of both health policy and the private sector to run it. Baroness Harding, the former chief executive of TalkTalk who heads up NHS Test and Trace, is tipped for the role.
The change will be “effective” within the next month but it will take until the spring to formally complete the organisational change of breaking up a large organisation.
A source said: “It will be in place by September.”
Sir Iain Duncan Smith, a former Tory Cabinet minister, welcomed the news, saying: “The one thing consistent about Public Health England is that almost everything it has touched has failed.”
The new institute – which will have tens of thousands of staff – will bring together the science expertise at PHE, which first published the genome of Covid-19, with the scale of NHS Test and Trace operation.
The model for the new institute is the Robert Koch Institute in Germany. The independent agency played a central role in the response to the Covid-19 pandemic, publishing daily situation reports that log new outbreaks, testing capacity and the current burden on the health system.
Approaches to tackling the crisis in South Korea have also provided evidence for Health officials in setting up the new body.
Over the next few months Test and Trace call centres will be wound down and replaced by local teams run by councils which are seen to be more effective and persistent at tracking down cases.
PHE’s work on tackling obesity will be handed over to local councils and family doctors, who are being encouraged increasingly to intervene to encourage fat people to lose weight.
In the medium term, the Health and Safety Executive, under its new chairman former Conservative MP Sarah Newton, will get a bigger role in assisting companies in getting more staff back to work.
PHE was originally set up in 2013 by then-Health secretary Jeremy Hunt as a result of an NHS shake-up organised by his predecessor Andrew Lansley.
The unprecedented challenge of the pandemic has exposed its weaknesses. Mr Hancock, who has been working on the overhaul for three months, had to take control of the Government’s testing strategy from PHE in March to scale up the numbers quickly.
One Government source said: “One of the many problems with PHE is that it has been spread too thin during the full pandemic.
“Instead of having an organisation that is constantly on alert for pandemics you have an organisation that has been concentrating on prevention of ill-health.”
There has also been a blame game in Whitehall with Health officials furious with PHE for counting all deaths from Covid-19, rather than just those within the first 28 days of contracting the virus, as in Scotland.
The body was also criticised for not having enough diagnostic testing capacity to properly track the progress of the epidemic in the early weeks of the outbreak.