The move will come into effect next week and will apply to anyone seeking to travel to England by air, sea or rail.
Shapps said the new rules would guard against the import of new strains of Covid-19, such as those detected in Denmark and more recently in South Africa.
Arrivals from non-travel corridor destinations will still be required to self-isolate for 10 days upon arrival, even if their pre-departure Covid status is negative.
Travellers will have to present evidence of their negative test result to their carrier upon arrival at their departure airport, as well as their completed passenger locator form.
UK Border Force will then conduct spot checks on arrival, with passengers subject to immediate £500 fines for non-compliance..
The Scottish government has confirmed it too will introduce a pre-travel testing requirement, and it is understood the UK’s devolved administrations in Wales and Northern Ireland are also looking at similar measures.
"We already have significant measures in place to prevent imported cases of Covid-19, but with new strains of the virus developing internationally we must take further precautions," said Shapps.
"Taken together with the existing mandatory self-isolation period for passengers returning from high-risk countries, pre-departure tests will provide a further line of defence – helping us control the virus as we roll out the vaccine at pace over the coming weeks."
The Department for Transport has said it will set out the required standard of pre-travel test and what proof passengers will need to present shortly.
Those arriving from travel corridor destinations who return a negative pre-travel Covid test result will still be able to take advantage of the government’s test to release scheme to cut their self-isolation requirement to as little as five days.
Limited exemptions from the pre-travel negative test requirement include hauliers, children under 11, crews, and those travelling from countries with limited testing infrastructure.
