He is the third person to have died since an outbreak of the disease began on May 23 in Edinburgh.
The man, who was in his 60s and from south west Edinburgh, had been unwell for a period of time and is considered to be part of the original outbreak.
The total number of confirmed cases remains at 50 and the number of suspected cases is now 49.
Health Secretary Nicola Sturgeon said: "My sincere condolences go to the family and friends of the patient who has passed away and my thoughts are with them at this very difficult time.
"Despite this sad and tragic news, is important to stress that strong evidence still suggests that all cases are associated with the suspected period of exposure and that the outbreak has peaked."
A Scottish Government update said that as of noon today, three patients are being treated in intensive care and six on general wards.
A total of 20 cases are being treated in the community, 57 have been discharged from hospital and three people have died. Ten cases are being treated outwith the NHS Lothian area.
The ages of the confirmed cases range between 32 and 85, with more males than females affected.
Ms Sturgeon added: "I repeat the message that anyone in the affected areas suffering from symptoms since the outbreak began should contact their GP or NHS 24.
"NHS Lothian are maintaining high-quality care for patients who remain unwell and work to identify and deal with the source of the outbreak continues."
Dr Christine Evans, consultant in public health medicine at NHS Lothian, said: "I would like to express my sincere condolences to the family of the patient who has died.
"We continue to see a small number of cases or suspected cases coming forward.
"I would like to reassure the public that this is in line with expectations. All of these patients have been ill for some time and have links to the south west of Edinburgh."
Lothian and Borders Police and the Health and Safety Executive (HSE) are jointly investigating the circumstances of the deaths.
HSE officials and Edinburgh City Council continue to investigate the possible source of the outbreak, thought to centre on a cluster of cooling towers in Wheatfield Road in the south west of the city.