The officers were on the scene before fire fighters at the fire in a flat on Seafield Road East in the city.
The pair attempted to enter the flat to save the 55-year-old occupant but were beaten back by smoke.
The fire broke out at around 1:30am on Sunday in the kitchen of a top floor flat.
Fire fighters rescued the 55-year-old man who was taken to the Royal Infirmary of Edinburgh and is described as being in a “serious condition”.
The two police officers were treated for smoke inhalation and were also taken to hospital.
A spokeswoman for Lothian and Borders Fire and Rescue said: “We were called to a flat alight at 1:36am.
“The fire started in the kitchen of a top floor flat.
“One hose reel and eight breathing apparatus were used and four pumping appliances and five special appliances were on scene.
“One male aged 55 was rescued by fire fighters and taken to hospital suffering smoke inhalation.
“Two police officers were also taken to hospital suffering smoke inhalation. They were on the scene when the fire brigade arrived.
A spokesman for Lothian and Borders Police said: “A 55-year-old male is in a serious condition at Edinburgh Royal Infirmary and two police officers were treated for smoke inhalation following a fire at a flat in Seafield Road East, Edinburgh.
“The fire was discovered shortly after 1:30 am on Sunday by a neighbour who called the fire service.
“Two police officers who attempted to enter the flat were beaten back by smoke and the male occupier was subsequently rescued by fire fighters who arrived shortly afterwards. There do not appear to be any suspicious circumstances.”