The two human cases are linked to nine cases of Mycobacterium bovis infection in cats in Berkshire and Hampshire last year.
Both people were responding to treatment, PHE said.
It said the risk of cat-to-human transmission of M. bovis remained "very low".
M. bovis is the bacterium that causes tuberculosis in cattle, known as bovine TB, and other species.
Transmission of M. bovis from infected animals to humans can occur by breathing in or ingesting bacteria shed by the animal or through contamination of unprotected cuts in the skin while handling infected animals or their carcasses.
The nine cases of M. bovis infection in cats in Berkshire and Hampshire were investigated by PHE and the Animal Health and Veterinary Laboratories Agency (AHVLA) during 2013.
The findings of the investigation are published in the Veterinary Record on Thursday.
Tuberculosis (TB) is an infectious disease caused by a germ which usually affects the lungs.
Symptoms can take several months to appear and include
•Fever and night sweats
•Persistent cough
•Losing weight
•Blood in your phlegm or spit
Almost all forms of TB are treatable and curable, but delays in detection and treatment can be damaging.
TB caused by M. bovis is diagnosed in less than 40 people in the UK each year. The majority of these cases are in people over 65 years old.
Overall, human TB caused by M. bovis accounts for less than 1% of the 9,000 TB cases diagnosed in the UK every year.
Those working closely with livestock and/or regularly drinking unpasteurised (raw) milk have a greater risk of exposure.
Public Health England
Screening was offered to people who had had contact with the infected cats. Following further tests, a total of two cases of active TB were identified.
Molecular analysis showed that M. bovis taken from the infected cats matched the strain of TB found in the human cases, indicating that the bacterium was transmitted from an infected cat.
Two cases of latent TB were also identified, meaning they had been exposed to TB at some point, but they did not have the active disease.
PHE said it was not possible to confirm whether these were caused by M. bovis or something else.
No further cases of TB in cats have been reported in Berkshire or Hampshire since March 2013.
Dr Dilys Morgan, head of gastrointestinal, emerging and zoonotic diseases department at PHE, said: "It's important to remember that this was a very unusual cluster of TB in domestic cats.
"M. bovis is still uncommon in cats - it mainly affects livestock animals.
"These are the first documented cases of cat-to-human transmission, and so although PHE has assessed the risk of people catching this infection from infected cats as being very low, we are recommending that household and close contacts of cats with confirmed M. bovis infection should be assessed and receive public health advice."
Out of the nine cats infected, six died and three are currently undergoing treatment.
Prof Noel Smith, head of the bovine TB genotyping group at the AHVLA, said testing of nearby herds had revealed a small number of infected cattle with the same strain of M. bovis as the cats.
However, he said direct contact between the cats and these cattle was unlikely.
"The most likely source of infection is infected wildlife, but cat-to-cat transmission cannot be ruled out."
Cattle herds with confirmed cases of bovine TB in the area have all been placed under movement restrictions to prevent the spread of disease.
Prof Malcolm Bennett, professor of veterinary pathology at the University of Liverpool, said occasional cases of TB in pets have always been seen.
"There seems to be an increase in the number of cases of bovine TB diagnosed in cats in recent years, and the report emphasises both the wide host range of these bacteria and that sharing our lives with other animals, whatever the benefits, carries some small risk.
"However, human infection, feline infection and transmission between the two remain rare," Prof Bennett said.
Prof Bertie Squire, professor of clinical tropical medicine at Liverpool School of Tropical Medicine, said it was important to put the two unusual cases in perspective.
"In 2012, there were 8,130 cases of human tuberculosis in England. In the same year there were only 26 notified cases of M. bovis in England, so M. bovis accounts for less than 0.5% of all human TB cases in the UK.
"The real problem of TB in the UK is caused by M. tuberculosis which arises in humans and is transmitted from person to person.  If we are to control human TB in the UK then we need to focus on identifying and curing the TB that occurs in humans, and we need to do this much better than we do at present.
"The real problem of human TB in the UK has nothing to do with M. bovis in cattle, badgers, or cats."
Two people in England have developed tuberculosis after contact with a domestic cat, Public Health England has announced.