Chris Froome suffered fractures in the vertebrae, a punctured lung and five broken ribs in the crash during training in France.
He was taken by ambulance helicopter to hospital in Toulon.
"He is in good spirits and grateful for the excellent medical care he has received", writes the Israeli team in a statement that has also been published on Chris Froome's Instagram account.
His team describes the operation as successful.
"Everything has gone as planned and Chris is recovering in hospital under the supervision of his medical team", writes the team.
Chris Froome won the Tour de France in 2013 and then three times in a row 2015–17.
