The change will come into force at 4am on Monday.
The minister said: “I don’t have any concerns about today’s international travel environment.
“The reason we are able to make these changes is because – first of all – our own vaccine wall of defence, with nine in 10 adults with a single jab, seven in 10 adults with two jabs.
“But also, the countries that are part of today’s announcement – the US and European countries – they also have very successful vaccination programmes.
“I think it’s very sensible, therefore, to say that if you have been double-jabbed – that’s going to be a clear requirement, it will be checked – you can come into the UK from amber list countries and not have to self-isolate.”
It will be a “boost to the economy” but it is “safe from a public health point of view”, Mr Javid added.
Javid: ‘no-one really knows’ future Covid trajectory after rise in cases
The Health Secretary, who previously warned there could be 100,000 daily cases over the summer, said he hoped recent falls in numbers would be sustained but it was important not to be “too optimistic”.
Speaking at a vaccination centre in London’s Little Venice, he said: “The truth is, when it comes to case numbers no-one really knows where they are going to go next.
“I hope that the falls that we’re seeing now are sustained. That’s of course what I want to see.
“But we’ve already seen with the Delta variant, a new variant that emerged over the last year, that’s more infectious than the previous one, that things can change.
“And so, I think it’s important to remain cautious, not get too optimistic.”