Hudson-Smith, 27, clocked 44.66 seconds to take the final podium place on Friday, behind American Michael Norman (24) and Kirani James (29) of Grenada.
"I had huge mental health issues in 2021," Hudson-Smith told reporters after winning Britain's fourth medal in Eugene, Oregon.
"Not a lot of people know this, but I literally attempted suicide.
"I was racing knowing I was hurt all the time, going to races knowing I'm not 100%... Imagine stepping on the line knowing you're hurt. You have a whole load of pressure because everyone expects a lot from you."
Hudson-Smith said he lost sponsors and got into financial debt while he was living in the United States as he struggled with injures and missed last year's Olympics.
"I couldn't do the Olympics for several reasons... During COVID, I was stuck in America by myself. I love America, but I wanted to be with my family. It was tough. I remember talking to a lot of people about not doing the sport.
"My mum and others were like, 'listen, just do this' and now I've paid the debts off, I got picked up by Puma and now I've got this medal... Honestly, a lot of people would have cracked."
Hudson-Smith said claiming his first world medal had restored his belief.
"I saw my name and I just dropped to the floor because these three years have been absolute hell," he said.
"This is my first chance for a medal on the world stage. A lot of people push on from here. Anything is possible."
