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.

Rudy also served as President Donald Trump's personal lawyer beginning in 2018 until he was disbarred in 2024.