People aged 25 to 29 who have not yet received a jab will be given the chance to secure a slot, Matt Hancock said, as the UK edges closer to meeting its target to offer all adults a first dose by the end of July.
Under 30s are the final demographic on the priority list of the biggest jabs rollout in NHS history.
Addressing MPs on Monday (7 June), Mr Hancock said vaccines were the key to breaking the link between coronavirus infections, hospitalisations and deaths.
More than half of all adults are now fully jabbed and more than three quarters have been given their first dose.
And from Tuesday, around three million more people will become eligible to book their first inoculation.
Mr Hancock said: “From this week we will start offering vaccinations to people under-30, bringing us ever closer to the goal of offering a vaccine to all adults in the UK by the end of next month.
“From tomorrow morning we will open up vaccination to people aged 25-29. Over the remainder of this week the NHS will send texts to people in these age groups and of course GPs will be inviting people on their lists to come forward.”
NHS England chief executive Sir Simon Stevens said: “Today is a watershed moment as the world-beating NHS vaccination programme enters the home straight of our race to offer everyone their first dose.
“The NHS vaccination programme is a real team effort and it is a testament to NHS teams across the country that we are able to open up to people in their 20s just six months on from delivering that world-first jab to Maggie Keenan.
“The tireless efforts of NHS staff to protect the people they care for and their communities has quite simply saved lives, and when you get the text, you’re next.
“Getting the lifesaving Covid-19 jab is the most important thing you can do, with NHS staff vaccinating at over 1,600 sites, including vaccine buses, places of worship, sport stadiums and other convenient locations. So when you get that text, book your appointment and join the millions who are already protected.”
Sped-up timetable for second jabs
Alongside opening up appointments to younger age groups, the health service is pressing ahead with offering second doses to people at pace.
The so-called race between variants and vaccines has led to a sped-up timetable for offering second jabs.
Instead of waiting 12 weeks for their second dose, people are now being invited back for their second dose after eight weeks.
It comes amid concerns over the spread of the variant first identified in India, also known as the Delta variant.
Only a handful of people have been admitted to hospital after having both doses of the vaccine, NHS leaders have said previously.
In Northern Ireland and most of Wales, all adults have already been called forward to get their vaccine.
Welsh First Minister Mark Drakeford said the programme would be extended to over-18s across the country before next week.
People aged 18 to 29 in Scotland have been asked to register for their jab, with appointments starting in mid-June.