Proud, 22, clocked 22.75 seconds in the sprint event with Brazil's Nicholas Santos second at 0.04 secs back while Andrii Govorov of Ukraine took bronze at 0.09 in a tight finish.
"At first I didn't realise I had won," admitted Britain's Proud, clearly shocked by his own victory.
"I was waiting for someone else to start celebrating, but when no one did, I looked on the scoreboard and saw my name on top."
Proud was born in London, but moved back to the UK from Kuala Lumpur, Malaysia as an 11-year-old to follow his dreams of becoming a pro swimmer.
"It's a weird feeling, this is something I've dreamt of since I started swimming," he said.
"It's the reason I moved to the UK.
"For it to happen today is amazing, I was never going to give up on that dream, I was going to keep going into my mid-30s."
Proud qualified as the fourth fastest from the semi-finals and the 2014 Commonwealth champion was an outsider for gold in Budapest.
"After last night I might not have looked in pole position, but deep down I knew if I got the start right, I'm in with a shout for the gold medal," he said.
"The past 24 hours have really been a mental battle getting my head in the right place, so I can race not even thinking about medals.
"It's really all about that first 15m, I just let my body takeover and switch my mind off.
"It took me a while to realise I'd won, I was shocked at first, it's a dream come true."
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