The Prime Minister told MPs on Wednesday the inquiry would take oral evidence under oath and place “the state’s actions under the microscope”.
Mr Johnson set a date of spring next year and confirmed he would consult Nicola Sturgeon on the scope of the inquiry.
He said: “Amid such tragedy the state has an obligation to examine its actions as rigorously and as candidly as possible, and to learn every lesson for the future, which is why I’ve always said when the time is right there should be a full and independent inquiry.
“So, I can confirm today that the government will establish an independent public inquiry on a statutory basis, with full powers under the Inquiries Act 2005, including the ability to compel the production of all relevant materials and take oral evidence in public under oath.
“So we will consult the devolved administrations before finalising the scope and detailed arrangements so that this inquiry can consider all key aspects of the UK response.
“This process will place the state’s actions under the microscope and we should be mindful of the scale of that undertaking and the resources required to do it properly.
"So I expect that the right moment for the inquiry to begin is at the end of this period in the spring of next year – spring 2022.”
Mr Johnson claimed the delay was over concerns about taking up health workers’ time.
He said: “This inquiry must be able to look at the events of the last year in the cold light of day and identify the key issues that will make a difference for the future.
“Free to scrutinise every document to hear from all the key players and analyse and learn from the breadth of our response.
“That’s the right way, I think, to get the answers that the people of this country deserve and to ensure that our United Kingdom is better prepared for any future pandemic.”
Mr Johnson also told the Commons that a commission on Covid commemoration would be established.
He said: “There is a solemn duty on our whole United Kingdom to come together and to cherish the memories of those who have been lost.
“Like many across this chamber, I was deeply moved when I visited the Covid Memorial Wall opposite Parliament.
"I wholeheartedly support the plan for a memorial in St Paul’s Cathedral, which will provide a fitting place of reflection in the heart of our capital.
“I also know that communities across the whole country will want to find ways of commemorating what we have all been through, so the government will support their efforts by establishing a UK commission on Covid commemoration.
“This national endeavour above party politics will remember the loved ones we have lost, honour the heroism of those who have saved lives and the courage of frontline workers who have kept our country going, celebrate the genius of those who created the vaccines and commemorate the small acts of kindness and the daily sacrifice of millions who stayed at home buying time for our scientists to come to our rescue.”
The announcement was welcomed by Labour leader Sir Keir Starmer, but he questioned why the inquiry could not start sooner.
He said: “I understand a statutory inquiry will take time to set up, but why could it not be later this year? Why could it not start earlier?”
Mr Johnson explained: “I think the House will agree that it would not be right to devote the time of people who are looking after us, who are saving lives, to an inquiry before we can be absolutely, much more certain than we are now, that the pandemic is behind us.
“I feel personally very, very strongly that this country has been through a trauma like no other, it is absolutely vital for the sake of the bereaved, for the sake of our country, that we should understand exactly what happened, we should learn the lessons – we have been learning lessons throughout – but we need to have a very clear understanding of what took place over the last 14 months.
“I think we owe it to the country to have as much transparency as we possibly can and we owe it to the country to produce answers in a reasonable timescale.”
Sir Keir also urged the UK Government to consult the families who had lost loved ones, as well as frontline workers.
He told the Commons: “Can I clearly welcome the independent inquiry into the pandemic and the establishing of a UK commission on Covid commemoration.
"Both are necessary, both will play an important part in learning the lessons and commemorating those we have lost.
“It is good that the government is consulting the devolved authorities, of course it is. But the government must also consult the families because this inquiry will only work if it has the support and confidence of the families.”
Liberal Democrats leader Sir Ed Davey said the commitment to a public inquiry was “welcome news”.
He said: “The PM must meet with the bereaved families immediately so they are at the very heart of this inquiry.”
The First Minister had previously said a four-nations inquiry into the coronavirus pandemic should begin this year.
Ms Sturgeon added she had already committed to an inquiry covering Scotland in 2021, but that a UK-wide inquiry could also look at issues affecting each nation.