Patel said the government recognised "how hard these changes will be for our travel and leisure sectors, who are already struggling through these unprecedented times".
The new measures will take effect on 8 June and be reviewed every three weeks.
"We’re taking this action at a time when it will be the most effective," Patel added. "Passenger arrivals are down 99% on last year and now we are past the peak of the virus, we must take steps to guard against imported cases to trigger another deadly surge of this disease.
"As transmission rate across the UK falls and number of arrivals begins to increase, the number of imported cases could begin to pose a larger and increased threat. We’re taking this action at a time when it will be the most effective."
Addressing enforcement of the quarantine rules, Patel said Public Health England would be carrying out checks to make sure arrivals were isolating, while those from overseas who refuse to comply may be refused entry into the country.
"Anyone breaking their 14-day quarantine could face a penalty of £1,000 – that will be a fixed penalty notice and could go into criminal prosecution," she added.
Director general of Border Force, Paul Lincoln, said the agency recognised the impact such measures would have on the travel firms, adding it would be working with the travel industry "on the detailed implementation in the coming days".