It is not known whether Schumacher is breathing spontaneously but it is believed that he will continue to be fed intravenously for some time to come. No detailed information was given on his condition or the form of his on-going treatment.
Schumacher has been in hospital since December 29 when he suffered a freak ski accident in the French resort of Meribel which left him brain damaged and fighting for his life.
In the last few weeks there has been widespread speculation that he is in a permanent vegetative state, meaning that he is clinically awake but unable to move or speak.
Last Friday there were rumours he was leaving intensive care and being transferred to a specialized rehabilitation clinic.
The German magazine Bunte said the driver's life was no longer in danger but his chances of making a full recovery appeared to have diminished.
Today Bild, Germany's biggest newspaper, said Schumacher was able to communicate with his family but it did not say to what extent or in what manner.
He has lost a quarter of his body weight since the accident and has had his muscles and joints massaged daily.
In today's statement issued by Ms Kehm she said: 'Michael has left the CHU Grenoble to continue his long phase of rehabilitation. He is not in a coma anymore.
'His family would like to explicitly thank all his treating doctors, nurses and therapists in Grenoble as well as the first aiders at the place of the accident, who did an excellent job in those first months.'
Referring to the thousands of messages of support from fans across the globe she added: 'The family also wishes to thank all the people who have sent Michael all the many good wishes to Michael. We are sure it helped him.
'For the future we ask for understanding that his further rehabilitation will take place away from the public eye.'
The spokesman for University Hospital Lausanne, Darcy Christen, said: 'The family are in a separate part of the hospital where their privacy can be best protected and where Michael Schumacher can obtain the highest level of care.'
The developments were welcomed by fellow sports stars on Twitter.
Arsenal and Germany forward Lukas Podolski wrote: 'What a great news!!! Get well soon Schumi!!! I'm so glad and happy when I just heard it!! #schumi #getwellsoon.'
Former England captain Rio Ferdinand tweeted: 'Schumacher out of coma & out of hospital.....just in time for Germany's 1st game of this World Cup. Inspiration.'
Schumacher's compatriots in the German football team will begin their World Cup campaign in Brazil against Portugal tonight.
The Mercedes F1 team, for which the driver raced in the last three years of his career, tweeted:
'Encouraging news on Michael's condition this morning. We couldn't ask for a better start to the week. #KeepFightingMichael.'
With an accumulated wealth estimated to be well over half-a-billion pounds, Schumacher's family is well placed to provide the limitless care that will be needed in the coming years. This will include physiotherapists, to massage his atrophying joints, doctors, nutritionists, nurses and neurological experts.
It was 24 weeks ago that Schumacher, a very competent skier, suffered his life-threatening accident.
He was holidaying with family and friends in Meribel, where he owns a chalet.
It was December 29 and a beautiful sunny morning. He hired a pair of new skis from a local ski shop to test them out. And he was wearing a helmet with a special camera attached to the front to record his morning's ski.
He was skiing with his 14-year-old son on a red piste, which is classed for intermediate skiers.
But shortly after 11am he left the piste and skied on to an off-piste area located in between the red run and a blue run, for beginners to intermediates.
It was here that he struck a partially-covered rock. He was not skiing fast but he lost control and catapulted 34 feet on to another rock.
He smashed his head on the bolder. The force of the collision shattered his helmet. The footage recorded on his helmet camera was undamaged.
THE REHABILITATION PROCESS
Doctors will now try to help Michael Schumacher cope with any disabilities he may have to help him achieve 'as much life function as possible', a neurologist has said today.
Dr. Tipu Aziz, a professor of neurosurgery at Oxford University's John Radcliffe Hospital, said: 'If he's been released from the hospital he was in, it means he's able to support his own breathing and bodily functions.'
He went on to say the fact that Schumacher is going into rehabilitation 'suggests there's been long-term side effects of his injury.'
He said: 'With rehabilitation, they'll try to train him to cope with the disabilities that he's got to achieve as much life function as possible.
'If he's had a brain injury, he may have weakness in his limbs secondary to loss of brain function. He may have problems with speech and swallowing.'
He said the fact the star was no longer in a coma suggests he is 'better than he was' but added: 'A full recovery is extremely unlikely.
'The fact he was in a coma for so long... we can assume that he has had quite a bad injury. People don't tend to make a full recovery from that sort of injury.'
- Daily Mail