The former New York City mayor is receiving the same drugs package that outgoing president Donald Trump got for the virus, he said during a radio interview from his hospital bed.
Mr Giuliani, 76, said he was “doing fine” and expected to be released from hospital on Wednesday morning.
"I have no fever. I have very little cough, it’s just about also gone, I’ve been walking around, and I think they’re going to let me out tomorrow morning," he said as he called into his own radio show.
But Mr Giuliani, who was hospitalised after attending a string of battleground events across the country without wearing a mask, said he still did not believe in mandates to enforce wearing them.
“I think you can overdo the masks, you can overdo almost anything,” he said.
“Everything done in moderation makes much more sense. And what we’re doing to American business right now is disgraceful, and it’s not based on science.”
Mr Giuliani said the White House doctor told him to seek treatment at Georgetown University Medical Center and to get remdesivir and dexamethasone, as the president had done.
“I didn’t wanna really go to the hospital, and he said, ‘Don’t be stupid. We can get it over with in three days,’” said Mr Giuliani.
“The minute I took the cocktail yesterday I felt 100 per cent better."
An estimated 15.1 million Americans have now tested positive for the virus and more than 285,000 people have died after being infected with Covid.
A second lawyer for Mr Trump has also tested positive for coronavirus, according to multiple reports.
Jenna Ellis, 36, has spent the past few weeks travelling the country with Mr Giuliani in an attempt to overturn election results for the president.
And on Friday she attended a Christmas party in the East Wing of the White House as the guest of the president’s trade advisor Peter Navarro.
Both Mr Giuliani and Ms Ellis have been accused of openly ignoring health guidelines laid down by the CDC to prevent the spread of the virus.
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