Officials believe the unidentified patient caught the virus, which proves fatal in 10 per cent of cases, in Nigeria before flying to England.
PHE said the first patient was diagnosed last week in Cornwall in the southwest of England and is being treated in London, while the second one was being treated at an expert respiratory infectious disease center in Liverpool.
Sufferers normally experience a rash alongside symptoms of fever, headache, aching muscles, backache, swollen lymph nodes, chills and exhaustion.
The first case in a human was discovered in the Democratic Republic of Congo in 1970, and since cases have been reported in central and west African countries. Unfortunately, there is no treatment that has been shown to be effective or safe.
Monkeypox is a rare viral infection that typically only leads to mild illness and does not spread easily between people, PHE said.
The second patient initially presented to the Blackpool Victoria Hospital and was transferred to the Royal Liverpool University Hospital after testing positive at the beginning of this week.
We know that in September 2017 Nigeria experienced a large sustained outbreak of monkeypox and since then sporadic cases have continued to be reported.
Although monkeypox and smallpox have similar symptoms, monkeypox is less deadly than smallpox: In previous outbreaks, the fatality rate for monkeypox has been between 1 percent and 10 percent, World Health Organization said.
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The unidentified patient had recently been to Nigeria, where they are understood to have picked up the disease.
"People without symptoms are not considered infectious but as a precaution, those who have been in close proximity are being contacted to ensure that if they do become unwell they can be treated quickly", the government agency has advised.
Transmission is via direct contact with infected animals, human, or contaminated materials.
Most people recover within several weeks, says PHE.
A rash can also develop, which usually starts on the face and spreads, forming a scab which falls off.
Monkeypox, which is related to chickenpox and smallpox, was first found in 1958 among laboratory monkeys.
Health officials said all necessary precautions were being taken by specialist staff in clinics where patients were being cared for, and said there was now no risk to other staff, patients or visitors.
Nigeria is experiencing a particularly virulent outbreak with 89 people infected and six deaths since 2017.
Symptoms usually appear about two weeks after a person is exposed to monkeypox.