Two-week quarantines will be imposed on new arrivals to the UK from 8 June with a £1,000 fine for anyone who breaches the measure.
The home secretary said during Downing Street's daily briefing that mandatory self-isolation would not apply to people coming from Ireland, medics tackling COVID-19 and seasonal agricultural workers.
The measure is aimed at preventing a new wave of coronavirus from overseas.
Passengers will have to fill in a form providing their contact and travel information so they can be traced if infections arise.
They will also be contacted regularly during the 14 days to ensure their compliance.
Those who breach the terms of self-isolation will be hit with a £1,000 fixed penalty notice in England or a prosecution with an unlimited fine.
Devolved nations can set out their own enforcement approaches.
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Border Force will be able to refuse entry to foreign citizens who are not UK residents during border checks, while removal from the country could be used as a last resort, the Home Office said.
Arrivals will be advised to use personal transport to head to their accommodation and once there not leave for 14 days.
They will also not be allowed to accept visitors, unless they are providing essential support, and should not go out to buy food or other essentials "where they can rely on others", the Home Office added.
The department said if accommodation does not meet necessary requirements, with hotels or with friends and family listed as options, the person will have to self-isolate in "facilities arranged by the government".
The Home Office also said arrivals would be encouraged to download the NHS contact-tracing app at the border "once rolled out nationally".
Priti Patel said: "As the world begins to emerge from what we hope is the worst of the coronavirus pandemic, we must look to the future and protect the British public by reducing the risk of cases crossing our border.
"We are introducing these new measures now to keep the transmission rate down and prevent a devastating second wave.
"I fully expect the majority of people will do the right thing and abide by these measures. But we will take enforcement action against the minority of people who endanger the safety of others."
The announcement is likely to anger the aviation industry, with airlines warning the measures could be disastrous for them.
Ministers were continuing to consider forging so-called air bridges with other nations that have low transmission rates in order to allow some international travel.
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