The British rider's bike hit a wall at speed during a reconnaissance ride for the fourth stage of the race in France.
The Team Ineos racer had been treated at the University Hospital of St Etienne, where he underwent a six-hour operation to repair a fractured right femur, broken hip, fractured elbow and fractured ribs.
Froome posted an update on Thursday afternoon as he prepared to begin the long road to recovery.
"As my time at ChuSaintEtienne has come to an end, I'd like to take the opportunity to thank the doctors & nurses for the exceptional care provided to me," Froome said on Twitter.
"It's been a rough week but I appreciate you having made it as comfortable as possible for me.
"This is just the first step to what will be a long recovery. Unfortunately I'm not yet able to go home, but at least I'll have an opportunity to get a visit from my kids".
Froome's teammate Geraint Thomas suffered an injury scare in a crash which forced him to withdraw from the Tour de Suisse earlier this week.
However, the 33-year-old Welshman remains optimistic about his chances of defending his Tour de France title when the action begins in Brussels on July 6.
But Team Sunweb's Tom Dumoulin will definitely miss the Tour because of a knee injury and a physically challenging run-up to the race, the Dutchman said on Thursday.
Dumoulin, 28, suffered a setback during recovery from a knee injury that forced him to abandon the Giro d'Italia last month.
The 2017 Giro d'Italia winner was expected to challenge defending champion Thomas which begins in Brussels on July 6.