Pre-departure Covid-19 testing will now be required for everyone travelling to England from 04:00 GMT on Monday.
The rules had been due to come into force on Friday, but the government said people needed time “to prepare”.
Those arriving by plane, train or boat, including UK nationals, will have to take a test up to 72 hours before leaving the country they are in.
Anyone arriving from places not on the UK’s travel corridor list must still self-isolate for 10 days.
Scotland is set to adopt the same approach to international travellers, while Wales and Northern Ireland are expected to announce plans for pre-arrival testing in the coming days.
Announcing the change on Twitter, Mr Shapps said: “To give international arrivals time to prepare, passengers will be required to provide proof of a negative Covid-19 test before departure to England from Monday 18 January at 4am.”
He also reminded travellers to fill out the Passenger Locator Form – used in track and trace – and added that those without proof of a negative test faced a fine of £500.
Problems with testing availability and capacity mean some countries will initially be exempt.
For instance, the requirement will not apply to travellers from St Lucia, Barbados, Antigua and Barbuda until 04:00 GMT on 21 January.
Travellers from Falkland Islands, Ascension Islands and St Helena are exempted permanently.
Hauliers are exempt to allow the free flow of freight, as are air, international rail and maritime crew.
The government has said all forms of PCR test will be accepted, as will other forms of test with “97% specificity, 80% sensitivity”.
