Joshua came face-to-face with Usyk for the first time since losing his WBA (Super), IBF, and WBO titles in London in September, BBC reported.
At a media conference, Joshua was full of confidence as he aims to become a three-time world champion.
"If you know my story, you know I'm the comeback king," Joshua, 31, said.
"You can put me down, but it's difficult to keep me down."
Joshua had his new head coach by his side, Robert Garcia.
The switch of trainer is one of many changes the Watford-born fighter says he has made for the rematch.
"In the fight in September, I was wrong and he [Usyk] was right," said Joshua who added that he had to "take that defeat like a man as well, I have to be accountable".
He added: "Definitely the hunger is still there. Blips happen, things happen in life, but resilience, mental toughness and consistency will always prevail."
Usyk has spent time in Ukraine helping the war effort against Russia and earlier in the summer it appeared the rematch would have to be postponed.
But the 35-year-old Ukrainian was given permission to leave the country in March to train for his second fight with Joshua.
Unbeaten in 19 professional fights, Usyk did not say much, only that he was fighting for Ukraine.
"We are not in the best conditions at the moment back home [in Ukraine]," he said.
"I never made some very loud and bright speeches, all I did was just work hard in my training camp, my gym, that's what I'm going do until the date of the fight."