The move, which allows fully vaccinated passengers arriving in England from countries not on the UK’s red list to take a cheaper lateral flow test instead of a PCR, came into effect on Sunday (24 October), in time for the half-term holidays.
Shapps said the change in rules will give passengers "more options and faster results".
"It’s thanks to the success of our vaccination programme that we can make this switch – giving the industry and consumers a much-needed boost," he added.
Health secretary Sajid Javid said the overhaul will make it "easier and cheaper" for people looking to book overseas holidays.
"I’m delighted that from today eligible travellers to England, who’ve had the life-saving Covid-19 vaccine can benefit from a cheaper lateral flow test, providing faster results," he added.
"This huge boost to the travel industry and the public will make it easier and cheaper for people to book holidays and travel abroad, and it is because of our incredible vaccine programme that this is possible."
He also confirmed that anyone who tests positive must then take a PCR test, which, if also positive, may be genomically sequenced to check for variants.
The UK government said the lateral flow tests must be taken "as soon as possible" on the day of arrival or, at the latest, before the end of a passenger’s second day.
The tests can now be purchased from a list of private providers on the government website, with prices ranging from £20 to £40. The portal was frequently unavailable when it launched on Friday (22 October).
Passengers who have already bought a PCR test to use for travel do not need to buy another test, as PCRs can still be used.
Travellers must take a photo of their lateral flow test and booking reference supplied by the private provider and send it back to them to verify the result.
Those who are not fully vaccinated returning from a non-red destination must still take a pre-departure test, a PCR test on day two and day eight and complete 10 days’ self-isolation.