Prominent buildings and landmarks will also be lit up.
More than 100 care organisations, charities, businesses, emergency services and community groups support the idea.
Mr Johnson said: “This has been an incredibly difficult year for our country. My thoughts are with all those who have lost loved ones, and who have not been able to pay tribute to them in the way they would have wanted.
“As we continue to make progress against the virus, I want to thank people for the sacrifices they continue to make, and hope they can look forward to being reunited with loved ones as restrictions are cautiously eased.”
Sir Simon said: “Coming out of the toughest year in the health service’s entire history, we need to reflect on the pandemic’s deep toll, mourn those we’ve lost, and mark the service and sacrifice of staff throughout the NHS.
“It’s also a moment to acknowledge how in adversity we saw strength, as friends, neighbours and communities have come together to help each other through the nation’s worst ordeal since the Second World War.
“While we need continuing vigilance against this virus, the remarkable NHS vaccination programme now brings hope of better times to come.”
Labour leader Sir Keir Starmer, Scottish First Minister Nicola Sturgeon and Welsh First Minister Mark Drakeford also support the idea which will see community-led activities such as virtual assemblies, choirs, services and yellow ribbons tied around trees.
A series of free online talks will take place featuring experts, bereaved families and celebrities, organised by the Good Grief Festival.
Marie Curie chief executive Matthew Reed said: “The last year has been one of the most traumatic and uniting in modern history. With so many of us losing someone close, our shared sense of loss is incomparable to anything felt by this generation.
“Many of us have been unable to say a real goodbye or comfort our family, friends and colleagues in their grief. We need to acknowledge that and recognise we are not alone.
“That’s why on March 23, it is important that we all come together to reflect on our collective loss, celebrate the lives of the special people no longer here, support those who’ve been bereaved and look towards a much brighter future.”