Hallyday left the hospital in Fort-de-France, on the French West Indian island of Martinique, in the small hours and boarded a private jet heading for Los Angeles.
He was to be taken to a hospital in Los Angeles, according to RTL radio which has enjoyed privileged links to the rocker for some years.
Although more admired France and Canada than in the English-speaking world, Hallyday has had a long and lucrative career.
The first concert of the Jimi Hendrix experience was in the French town of Evreux in 1966, when they opened for him.
British rockers Jimmy Page, Peter Frampton and the Small Faces all played on his albums in the 60s.
Eagle-eyed journalists suspected his departure was imminent on Thursday afternoon when a hairdresser entered the hospital by a side door. The star’s wife, Laeticia.had already arrived in the morning.
Hallyday was transferred to the hospital on Monday from another in Point-à-Pitre after being taken ill at a home he owns on the jet-set island of Saint-Barthélemy.
Doctors are staying mum about the reason for his hospitalisation but his entourage has said that it was a breathing problem, while he at one point tweeted that it was bronchitis.
On Wednesday he posted a message on Instagram to guitarist Brian Ray, assuring him in extremely colloquial terms that he would soon be back in the studio to “slay” an album they are to record.
But, given the length of his stay in hospital, French media are speculating that he may not be in good enough to continue his 2012 tour, whose second leg is due to kick off with the Montreal gig.