Between them, the two doctors worked in four different places in East and West Sussex - a nursing home, an A&E department and two GP practices.
The pair are now in isolation, and efforts to trace those that came into contact with them are ongoing.
The GP practices, in Brighton, have now reopened after a deep clean.
Worthing Hospital, where one GP worked a shift in A&E, continues to operate as normal, a Department of Health spokeswoman said.
The nursing home - Patcham Nursing Home - has closed to visitors as a precaution, but nobody there is reported to be unwell.
One of the Brighton doctors has been named as Catriona Greenwood. She was infected by Steve Walsh, from Hove, who caught the virus in Singapore before staying with her and a group in a chalet in France.
The second GP has not been named.
Speaking out for the first time on Tuesday, Mr Walsh said he had "fully recovered" from the virus, but remained in quarantine.
The total number of people with coronavirus in the UK is eight. There are six cases from the Brighton area - Steve Walsh plus five others - and two cases, both Chinese nationals, who were staying in York.
They are all being treated in specialist NHS units in hospitals in London and Newcastle.
On Tuesday, the World Health Organization said the official name for the disease caused by the coronavirus is Covid-19.
Prof Neil Ferguson, infectious disease expert from Imperial College London, told the BBC that he thought new cases of the virus could still rise.
"I think we're in the early phases of a global pandemic at the moment," he said.
Prof Ferguson added it was likely that only one in three cases coming into the UK was being picked up.
But John Oxford, emeritus professor of virology at Queen Mary University London, said he thought the virus had a weakness - and people's actions could help slow transmission.
"It's not about wearing a mask - it's less of the hand-shaking, touching and kissing," he said, speaking on the Today programme.
What are the symptoms of coronavirus and what can help stop its spread?
The main signs of infection are fever (high temperature) and a cough as well as shortness of breath and breathing difficulties.
Frequent hand washing with soap or gel, avoiding close contact with people who are ill and not touching your eyes, nose and mouth with unwashed hands, can help cut the risk of infection.
Catching coughs and sneezes in a tissue, binning it and washing your hands can minimise the risk of spreading disease.
Anyone experiencing symptoms, even if mild, after travelling from mainland China, Thailand, Japan, Republic of Korea, Hong Kong, Taiwan, Singapore, Malaysia or Macau, is advised to stay indoors and call the NHS 111 phone service.
On Monday, the government issued new powers in England to keep people in quarantine to stop the virus spreading.
Under the Department of Health measures, people will not be free to leave quarantine and can be forcibly sent into isolation if they pose a threat.
As of Tuesday evening, a total of 1,358 people have been tested for coronavirus in the UK.
The BBC understands that two prisoners on a wing at HMP Bullingdon in Oxfordshire have been tested for the virus. One of them, a remand prisoner, had recently returned to the UK from Thailand.