Robert Kubica's elbow surgery on Wednesday took eight hours, the Santa Corona hospital near Genoa has confirmed.
"The operation was a success and it will probably not be necessary for him to undergo further surgery," the Italian hospital said in a statement.
It is believed that Kubica, 26, will probably need to stay in hospital for a further 10 to 15 days, initially in intensive care.
He will then begin his rehabilitation in Italy.
"The elbow was rebuilt satisfactorily but it is harder to give a prognosis about the recovery of functionality," orthopaedics head Francesco Lanza is quoted by La Gazzetta dello Sport.
Before the operation, the Polish driver was interviewed by Savona police as they investigate his horror crash in the Ronde di Andora rally.