Dr Duncan McCormick from NHS Lothian told ITV News that although all the evidence points towards 'no further exposure' to the Legionella infection, those with underlying health problems who are already affected will take longer to recover.
NHS Lothian report that the number of confirmed cases is still 41, with 48 suspected cases, taking the total number of overall cases to 89.
A second person was confirmed dead after contracting the disease in Edinburgh, but has not yet been named.
Terry Holeran "wants answers" after he contracted Legionnaires' disease and had to be treated at Western General Hospital in Edinburgh.
The 55-year-old said he has instructed specialist illness lawyers to help him find out how the outbreak occurred and what can be done to prevent it from recurring.
Mr Holeran said: "It has been one of the worst weeks of my life. I'm just so angry about the whole thing and want to know what went wrong to cause the outbreak.
He became ill on June 5th with aches and pains, tiredness and breathlessness. He was treated at Western General Hospital where doctors sent him home with antibiotic treatment.
There are now 40 confirmed cases of Legionnaires' Disease and 48 suspected cases.
Whilst we realised that further deaths were a possibility this additional death is extremely sad and I would like to express my sincere condolences to the family of the patient.
My sincere condolences go to the family and friends of the patient who passed away in Edinburgh tonight in a case linked to the outbreak of Legionnaires' disease in the city. My thoughts are with them at this very difficult time.
Despite this sad and tragic development, it remains the case that we believe the outbreak to have peaked. However, we continue to monitor the situation carefully and advise anyone with any concerns to contact the special NHS 24 helpline on 08000 85 85 31.
The man, who had significant pre-existing underlying health conditions, died earlier on Thursday evening in Edinburgh Royal Infirmary.
The health board said that he was one of the confirmed cases in the outbreak, which began in the Scottish capital at the beginning of June.
The first man to die was named as Robert Air, 56, from the Seafield area of the capital, whose death was reported on June 5.
A second person has died after catching Legionnaires' disease during a outbreak in Edinburgh, NHS Lothian said.
Cases of a deadly outbreak of Legionnaires' disease in Scotland have risen again, the Scottish Government has confirmed.
There are now 82 confirmed and suspected cases of Legionnaires' disease from the outbreak in the south-west of Edinburgh.
This is an increase of one in the total number of confirmed cases, taking the number to 37, and an increase of one suspected case from yesterday, taking the total to 45.
The Health and Safety Executive and Edinburgh City Council are continuing their investigations into the possible source of the outbreak.
Cases of a deadly outbreak of Legionnaires' disease have risen again, the Scottish Government's Health Secretary has confirmed.
There are now 80 confirmed and suspected cases of Legionnaires' disease from the outbreak in the south-west of Edinburgh.
This is an increase of eight in the total number of confirmed cases and a decrease of two suspected cases.
Ensuring the health and safety of our employees and the local community is our highest priority. On Thursday 7 June we voluntarily took our cooling towers off-line until the legionella results from samples taken earlier this week are reported. While this precautionary operation is under way we have temporarily ceased distillation. Industrial cooling towers remain only one potential source of the infection and North British Distillery is one of a number of sites with such towers in Edinburgh.
We continue to work closely with the HSE and all other relevant authorities in relation to this issue. North British Distillery would like to reaffirm that the Improvement Notice issued by the HSE today does not mean that this cooling tower has been identified as the source of the outbreak.
There are now 74 confirmed and suspected cases of Legionnaires' disease amid an outbreak in the Scottish capital.
Scottish Health Secretary Nicola Sturgeon has said the increase of 13 in the total number of confirmed and suspected cases had been expected.
Twenty-eight people have now been confirmed as having Legionnaires' disease and another 46 are suspected of having it.
So far one man has died, named locally as 56-year-old Robert Air, from Seafield in Edinburgh.