Some good news for Rudy Giuliani … he’s back to breathing on his own after being on a ventilator.

Rudy’s doctor hopped on Fox News and provided a positive health update for the former New York City mayor … saying he’s doing much better Monday after having a priest come to the hospital and anoint him.

As we reported on Sunday … 81-year-old Rudy was rushed to a Florida hospital in critical condition … suffering from a bout with pneumonia.

This is the second time Rudy has been hospitalized in recent months … back in September, Rudy was rushed to the hospital after sustaining serious injuries in a car crash. Sounds like Rudy will be back to shopping for hair dye in no time.