The front page headlines sparked a storm of criticism, and he formally quit tonight.
He also publicly apologised to his family.
The Health Secretary was under growing pressure to resign after the story broke in The Sun, and a video of the embrace in a government building was then leaked online.
Mr Hancock had apologised for breaching social distancing rules, and Boris Johnson, Prime Minister, said he considered the matter closed.
But this evening, married Mr Hancock bowed to the inevitable and tendered his resignation.
In a letter to the Prime Minister he said the Government "owe it to people who have sacrificed so much in this pandemic to be honest when we have let them down.”
He said: "The last thing I would want is for my private life to distract attention from the single-minded focus that is leading us out of this crisis.
"I want to reiterate my apology for breaking the guidance, and apologise to my family and loved ones for putting them through this. I also need (to) be with my children at this time."
In a letter in response to Mr Hancock's resignation, the Prime Minister paid tribute.
He wrote: You should leave office very proud of what you have achieved - not just in tackling the pandemic, but even before COVID-19 struck us.
"Above all, it has been your task to deal with a challenge greater than that faced by any of your predecessors, and in fighting COVID you have risen to that challenge - with the abundant energy, intelligence and determination that are your hallmark.
"You should be immensely proud of your service. "He added: “ am grateful for your support and believe that your contribution to public service is far from over."