A total of 16 cases were being treated in the community, 19 have been discharged from hospital and one person has died.
Health Secretary Nicola Sturgeon said: "These latest figures are reassuring and in line with expectations, and although it is too early to be definite they do suggest we are now in the later stages of this outbreak.
"All those involved are responding extremely well: NHS Lothian services are coping with the demands on them and the City of Edinburgh Council and the Health and Safety Executive continue to make significant progress in their investigation to identify the source of this outbreak."
Five of the cases are being treated outside the NHS Lothian area. One patient is being treated in the north of England, two in NHS Tayside, one in NHS Lanarkshire and one patient from NHS Highland is now being treated in Glasgow. At this stage all these cases are considered to be linked to the south-west Edinburgh outbreak.
The ages of the confirmed cases ranges between 33 and 76, with more males than females affected. NHS 24 has received 630 calls to the dedicated helpline for Legionnaires' disease. One man has died, named locally as 56-year-old Robert Air, from Seafield in Edinburgh.