The four-times Tour champion sustained multiple fractures including broken femur, elbow and rib bones when he crashed at high speed while checking the course ahead of the individual time trial on Wednesday.
The 34-year-old Briton was airlifted to the University Hospital of St Etienne, where he is continuing his post-surgery recovery.
"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," Froome said in a statement.
“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.”
Froome offered his thanks for the overwhelming number of messages of support from fans.
“This is obviously a tough time but I have taken a lot of strength from the support over the last three days,” he added.
“The outpouring of support has been really humbling and something I would never have expected.”
Froome's teammate Wout Poels won the queen stage of the Dauphine and dedicated his win to his fallen teammate.
"It was hard to see what happened to Chris," said Poels, "obviously I was behind it when it happened, it gave me a little bit more motivation as he should be the leader, but then I had to take over. It’s really nice for the team to get a nice win and and it’s a gift for Chris."