"The diagnosis is thus one of a near-syncope caused by sustained effort during hot weather, without loss of consciousness, in the context of fatigue linked to a heavy workload," the Elysee Palace said.
Doctors have recommended that Sarkozy, who left the Val de Grace hospital on Monday morning, spend several days resting to recuperate from the incident.
Sarkozy collapsed on Sunday while jogging in the wooded parkland around the Palace of Versailles just outside Paris, the French capital.
His bodyguards and his official doctor, running alongside him, were able to help him lie him down.
His wife, Carla Bruni, raced to the scene of the incident on a police motorbike, a witness told the AFP news agency.
Sarkozy, who assumed the presidency in May 2007, is a fitness enthusiast, and is often seen jogging or cycling with aides and bodyguards.
Just over three weeks ago, the Elysee Palace released the findings of Sarkozy's latest annual health check, describing the results of recent blood and heart tests as "normal". No further details were provided.