"The cough's gone. The cold's 90% gone. I'm happy," the tennis great told reporters Saturday.
"The last couple days I've been able to practice normally. I'm relieved that since Thursday now I'm better."
An ailing Federer lost in the final of his opening 2016 event in Brisbane, where he was defending champion.
The 34-year-old was beaten by Milos Raonic -- the former charge of his new coach Ivan Ljubicic.
The Croatian, once one of Federer's on-court rivals, has taken the place of the Swiss star's idol Stefan Edberg, who ended their two-year working relationship.
"We always got along well," Federer said of Ljubicic, who also served with him on the ATP Player Council.
"That was an important phase because I needed to trust Ivan there on the entire board change we were going through. It was quite tricky, not a comfortable thing to do. I had to work very closely with him.
"Towards the end of the career when he had family, I had family -- we also spent more time together. We always stayed in touch. I was happy for him when he did as well as he did with Milos as a coach."
Federer hopes Ljubicic can help him end Novak Djokovic's dominance, having won three of their eight meetings in 2015 -- losing five finals.
"Last year I did quite well against Novak. Of course, I've got to keep it up," he said.
"I always believe there's new things you can learn, but there's always sometimes a way of staying motivated, staying hungry. Someone like Ivan can also help do that.
"I can do a lot by myself, but I need my support team to push me the last 1%, 5%, 10%, whatever it is, because I'm not in the same mood every single day."
Melbourne Park had been a happy hunting ground for Federer -- until last year, when he lost to Andreas Seppi in the third round, his earliest exit since 2001.
Four of his record 17 grand slam titles have come in Australia -- the last of which was in 2010 -- while he has also been runner-up once and a semifinalist on six occasions.
"The Australian Open is the one where players come in maybe most inspired," said Federer, who opens his campaign Monday with an evening match against 117th-ranked Nikoloz Basilashvili of Georgia.
"It's also been my most consistent slam maybe until last year. I always played very well here. I don't know if it's the conditions or the court speed. It's a good place for me to start the year."
World No. 1 Djokovic starts his title defense Monday against South Korea's 51st-ranked Hyeong Chung, as the Serbian seeks his sixth Australian success and 11th grand slam overall.
In the women's draw, defending champion Serena Williams plays 35th-ranked Italian Camila Giorgi while last year's runner-up Maria Sharapova takes on Japanese No. 58 Nao Hibino.
WTA Finals winner Agnieszka Radwanska of Poland is up against American Christina McHale, and two-time Wimbledon champion Petra Kvitova faces Thai qualifier Luksika Kumkhum.