Mr Hancock said that the move came as the UK passed the milestone of giving a first dose of vaccine to four out of five adults.
He told the annual conference of the NHS Confederation that the speed and scale of protection offered to people across the country was “an incredible achievement”.
Mr Hancock said that it was “remarkable” that the UK had been able to reach this point within six months of the first non-experimental vaccinations in December and the peak of the second wave of Covid-19 in January.
He told the conference: “We’ve come such a long way since then, to the point that I can confirm that, as of today, we have given a first dose of vaccine to four out of every five adults in the United Kingdom.
“And the speed of deployment means that tomorrow we can open vaccination to everyone over the age of 18.
“I think it’s an incredible achievement.”
Mr Hancock said that, while there were still just over 1,000 Covid patients in hospital, “we know that the vaccine is our way out of the pandemic”.