The four-time Tour de France winner crashed at close to 35mph during his fourth-stage reconnaissance at the Criterium du Dauphine on Wednesday.
"I know how lucky I am to be here today and how much I owe to all the paramedics and medical staff on the race," said Froome in a post published on the Team Ineos website.
"Whilst this is a setback and a major one at that, I am focusing on looking forward. There is a long road to recovery ahead, but that recovery starts now and I am fully focused on returning back to my best."
The post was issued with a picture of Froome giving the thumbs up from his bed at the University Hospital of St Etienne, where he has been receiving treatment.
It has been reported that Froome suffered a fractured neck and faces six weeks in hospital. He also has a broken femur and broken ribs, and is not expected to compete again this year.
The first thing the champion cyclist wanted to know after undergoing surgery while in intensive care was how quickly he could begin his rehabilitation, according to the doctor who performed the surgery.
Rémi Philippot told ITV News Sports Editor Steve Scott: "I was very surprised because he feels very good, he is totally conscious about the trauma.
"The first thing he wanted; he wanted to know if he can already begin the rehabilitation, so it's very surprising."