Grant Shapps said post-arrival lateral flow tests will no longer be required as restrictions were "firmly placed in the past".
He told the UK parliament the move would help the aviation industry to "take back to the skies".
Shapps told MPs that the definition of fully vaccinated as "two doses of an approved vaccination or one dose of a Janssen vaccine" would remain for now.
But that the rules for those who did not count as fully vaccinated would change too.
He said: "We'll go further, the measures for those arriving in the UK who do not qualify as fully vaccinated have not changed since last March, so the time has come to review that position too.
"Today, I can announce that passengers who do not qualify as fully vaccinated will no longer be required to do a day eight test after arrival, or indeed to self-isolate.
"They will still need to fill out a passenger locator form to demonstrate proof of a negative COVID test taken two days before they travel and they must still take a post-arrival PCR test.
"This is a proportionate system that moves us a step closer to normality while maintaining vital public health protections."
He said the government intends to move away from "blanket border measures" to a "more sophisticated and targeted global surveillance system".
Earlier, the prime minister said the rules could be lifted because the country was "moving through the Omicron wave".
Boris Johnson said: "So what we're doing on travel, to show that this country is open for business, open for travellers, you will see changes so that people arriving no longer have to take tests if they have been vaccinated, if they have been double vaccinated."
Shapps said: "We promised we wouldn't keep these measures in place a day longer than was necessary and it's obvious to me now that border testing for vaccinated travellers has outlived its usefulness, and we're therefore scrapping all travel tests for vaccinated people.
"Not only making travel much easier but also, of course, saving about £100 per family on visits abroad, providing certainty to passengers, to carriers and (the) vital tourism sector for the spring and the summer seasons."
And he added this would help "ensure that 2022 is the year in which restrictions on travel, on lockdowns and limits on people's lives are firmly placed in the past".
The changes will come into effect from on February 11.
Shapps also told MPs the UK is also set to recognise vaccine certificates from 16 further nations.
He said reconnecting to key markets will not only "boost" the UK economy but also help the aviation industry to "take back to the skies".
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