Four-time Tour de France champion underwent a six-hour operation. He remains in France for intensive care.
Froome was ruled out of the competition following a crash at the Criterium du Dauphine. He sustained multiple bone fractures and a broken femur.
“Chris woke up this morning and was reviewed by intensive care consultants and the orthopaedic specialist who operated on him and they’re both very happy with his progress,” team doctor Richard Usher said in a statement.
Froome, who was born in Nairobi, Kenya, thanked the fans for their support.