NHS and social care workers marked the solemn anniversary at midday, as did MPs and peers in both Houses of Parliament and ministers in the devolved nations.
Cathedrals in Blackburn, Winchester, Gloucester and York Minster also fell silent in honour of those who have died during the pandemic.
The Queen reflected on the "grief and loss felt by so many" as she paid tribute to the service of health and care workers in a message to St Bartholomew's Hospital, where the Duke of Edinburgh had heart surgery.
Blackpool Tower, the Scottish Parliament, Belfast City Hall, The London Eye, Tate Britain and other buildings will be lit in yellow on Tuesday evening to mark the occasion.
The public is also being urged to stand on their doorsteps at 8pm with a candle or light.
The Prime Minister, who has offered his "sincere condolences to those who have lost loved ones", observed the minute's silence privately.
It came on the day new figures from the Office for National Statistics showed a total of 149,117 people have had Covid-19 recorded on their death certificate since the pandemic began.
Earlier, Downing Street said Mr Johnson had reflected with Cabinet ministers on Tuesday morning on what had been "a very dark and difficult year" for the nation.
A No 10 spokesman said: "The PM said that we mourn all those we have lost and send our deepest sympathies to their families, friends and loved ones.
"The PM said the last year had also shown the great strengths of the British public, which had demonstrated such resilience and fortitude and had shown such willingness to work together for a common good.
"The PM and Cabinet paid tribute to the extraordinary service of everyone in the NHS, social care and in the public sector over the past year, along with all those who had kept the country going - from bus drivers to shop workers.
"The PM said the ability of British scientists to respond to the pandemic had been incredible.
"He said that, if asked last March, he would not have believed it would have been possible to have developed a vaccine and delivered it to half of the UK adult population within 12 months.
"The PM said this was an absolutely astonishing achievement, which is a tribute to British science but also to British business."