The new series, which has yet to be named, will “tell the true story of the biggest national and personal crisis to face a government leader since World War II,” Fremantle, Passenger and Revolution Films said in a joint statement.
Mr Johnson has come under fire for the Government’s response to the coronavirus pandemic on several fronts.
The UK has the highest death toll in Europe and the second highest numbers of deaths per capita in the world, although countries have been recording fatalities in different ways.
Mr Johnson’s government has been criticised for delaying the decision to go into lockdown – a move which opponents say may have cost thousands of lives.
Critics have also slammed the Government for shortages in personal protective equipment (PPE) provided for NHS and care staff, with multiple reports of healthcare workers being provided with inadequate PPE.
The Prime Minister came close to death himself in April, after being hospitalised in an intensive care unit.
But there was also positive news, as his fiancee Carrie Symonds gave birth to a son in May.
Fremantle chief operating officer Andrea Scrosati said: “There are rare moments in history when leaders find their private lives uniquely connected to national events, where personal experience and official role collide in an unusual way
“The last few months in the life of the UK Prime Minister clearly mark one of these moments.”
As well as the Trip series, Mr Winterbottom has directed an eclectic range of films in his career. His most recent film is Greed, a scathing satire of Britain’s leading clothing retailers.
Co-producer Richard Brown added: “Michael Winterbottom is the ideal filmmaker to tell the story of the extraordinary events surrounding Boris Johnson’s new government and the Covid-19 pandemic, which has captured the attention of the world.”