It was reported last night that when he arrived there doctors were worried he would not survive. But after a few days in hospital he was allowed to move to a hotel where his condition was monitored.
His two eldest children Marlon, 36, and Angela, 34, from his relationship-with Anita Pallenberg, have flown from Britain to join Patti and her two daughters with Keith, Alexandra, 19, and Theodora, 21.
The injury is believed to be a subdural haematoma, a blood clot that forms in the outer membranes of the brain, often from a torn vessel. It can be caused by a fall or a blow to the head.
A London neurosurgeon said yesterday: 'If you have a bad fall then it can severely shake the contents of the brain, causing micro-damage to the blood vessels.
'Sometimes pressure can build up in those vessels and they can leak, causing a clot. Doctors may have to drill through the skull and lift up the skull and expose the portion where the clot may be.
'Once it is isolated it can be secured with a clip or a tie and the head is then sewn back together. This is a serious operation and the quickness of recovery depends on the age and health of a patient.
'I would be surprised if anyone could be back on stage within a few weeks, although it is not an impossibility.'
Richards is notorious for living on the edge. He has abused his body with drink and drugs for four decades and often pokes fun at his reputation when he arrives on stage with the line: 'Good to be here, good to be anywhere.'
The Stones' Bigger Bang tour was due to open in Barcelona on May 27 and end in England in August. The band's management were working feverishly on a revised schedule last night.