Mr Johnson said he would consult Nicola Sturgeon on the inquiry’s scope, and the First Minister has welcomed the move, while calling for it to be brought forward.
The inquiry is set to be launched in spring next year as the government expects a possible further surge of Covid-19 cases in the winter.
Mr Johnson said the government was "fully committed to learning the lessons at every stage of this crisis", and Ms Sturgeon added that it should cover “all aspects of the impact and handling of the pandemic”.
It is likely to be broad in scope and could take several years to complete.
The period under scrutiny stretches from before the first cases of Covid-19 were identified, as a key aspect of the UK’s response to the crisis was general preparations for the event of a pandemic.
The UK drew up a pandemic preparedness strategy in 2011, including the four nations, and Scotland took part in three training exercises in the years afterwards.
However, later reports found that not all the learnings from these were put into place, and that this may have led to PPE shortages in the early months of 2020.
Pressures on social care will also be a key issue, with care homes particularly relevant in Scotland.
Thousands of elderly patients were discharged from hospitals to care homes in the early months of the pandemic to free up hospital beds, in a move the Scottish Government later admitted was a “mistake”.
The exposure of health inequalities is also likely to come up, with the pandemic having had a disproportionate effect on minority ethnic and lower income communities. This is also related to support for workers and those told to self-isolate.
International travel will be another area of concern.
The UK did not close international borders for many months, despite repeated calls for this to happen, and Ms Sturgeon has said she wishes Scotland had been “much tougher” on the border with England as case numbers fell in Scotland in the summer.
There will be positive aspects to the inquiry too, and the speed and success of the vaccination programme is likely to stand out among these.