It is believed that the cats were infected with the disease after contact with wildlife, such as badgers or rats, although cat-to-cat transmission could not be ruled out.
Cattle herds with confirmed cases of bovine TB in the area were all placed under movement restrictions to prevent the spread of disease. In England, any farm which has cattle that test positive for bovine TB is banned from moving animals off the farm until two consecutive clear tests are completed over a period of 120 days.
The outbreak in Berkshire and Hampshire was identified in nine cats in 2013, the AHVLA said.
PHE said that screening was offered to 39 people who may have had contact with the infected cats.
A total of 24 people accepted the screening.
Two cases of active TB and two cases of latent TB were identified.
The general risk of cat-to-human transmission remains "very low" according to PHE experts.
Professor Noel Smith, Head of the Bovine TB Genotyping Group at AHVLA, said: “Testing of nearby herds revealed a small number of infected cattle with the same strain of M.bovis as the cats.
"However, direct contact of the cats with these cattle was unlikely considering their roaming ranges.
"The most likely source of infection is infected wildlife, but cat-to-cat transmission cannot be ruled out.”
Humans can catch TB by inhaling or ingesting bacteria shed by the infected animal or through contamination of unprotected cuts in the skin while handling them.
NFU Deputy President, Minette Batters, said: “We express our sympathies to those people who have contracted TB through their cats.
"We understand that the source of infection was wildlife – either badgers or rats.
"Badgers are known to spread TB amongst cattle and this latest news that they may have infected cats which have gone on to infect humans underlines the pressing need to control the spread of TB in wildlife.”
There have been no further cases of TB in cats reported in Berkshire or Hampshire since March 2013.
Molecular analysis at AHVLA showed that M.bovis isolated from the infected cats and the human cases with active TB infection were indistinguishable, which indicates transmission of the bacterium from an infected cat.
In the other cases of latent TB infection, it is not possible to confirm whether these were caused by M.bovis or the source of their exposure.
Dr Dilys Morgan from PHE said:“It’s important to remember that this was a very unusual cluster of TB in domestic cats.
"Mycobacterium 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 that 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 confirmedM.bovisinfection should be assessed and receive public health advice.”
Local human and animal health professionals are remaining vigilant for the occurrence of any further cases of disease caused by M.bovis in humans, cats or any other pet and livestock animal species.