Smiling for reporters he held up his NHS vaccination card and knocked elbows with Professor Van-Tam.
Mr Hancock tweeted a picture of the moment he was given his first dose, describing the process as quick and painless.
He said he was “very excited” when he was called for the jab and encouraged everyone invited for a Covid-19 vaccine to take up the offer.
Alongside a picture of himself getting the injection from a masked Professor Van-Tam, he wrote: “Brilliant! Got the jab. In & out in 8 minutes. Didn’t hurt at all. Massive thanks to JVT & the @sciencemuseum team. When you get the call, get the jab!”
In a further statement he said it had been “a privilege to get my first jab within the historic walls of the Science Museum in London, where the team are documenting the national pandemic response and preserving items like the first Covid-19 vaccine vial to be used anywhere in the world”.
He paid tribute to learning from science, saying it had been “central this last year more than ever” and that it therefore “felt fitting to be at the museum”.
He added: “Over 47 million doses have now been administered across the country thanks not only to hundreds of hospitals, GP clinics and pharmacies, but to incredible sites like this that have volunteered their unused spaces.
“The rollout continues at pace and we are on track to reach our target of offering all adults a first dose of the vaccine by the end of July.
“I was very excited when my call came, and I’d urge everyone to take up the offer when it comes, and become part of history in the UK’s biggest ever vaccination programme.”
Yesterday Professor Van-Tam revealed the UK had very low levels of Covid-19 and that the number of people in hospital due to the virus is expected to drop further.
He said the “disappearance of our third wave” was thanks to the public following restrictions, while the vaccination programme had “undoubtedly helped” in recent months.
Speaking at a Downing Street press briefing Prof Van-Tam said: “We are really in very low levels that are comparable to where we were in September last year.”
He also said that scientifically it would be safe for vaccinated people to meet, but suggested the reason why they are currently prevented from doing so is because younger people have not had a vaccine.
Professor Van-Tam added: “If two people who both had two doses of vaccine and have both served at least 14 days after their second dose, then I would be highly confident scientifically that if they were reputable vaccines then indeed it would be incredibly safe for those two people to meet.”
On when that could happen in the UK, he said: “Soon, I really hope soon, but not quite now.”
He warned that nobody under 42, apart from the clinically extremely vulnerable “in whom the vaccine may be slightly less effective” and healthcare workers, have had the vaccine.
Indoor meetings between vaccinated people are already happening in the US.
On Wednesday the Government announced that 60 million doses of the Pfizer BioNTech coronavirus jab had been secured for a booster vaccination programme in the autumn.