Australian Browne stopped defending champion Ruslan Chagaev to win the title in Russia earlier this month.
The 36-year-old delivered a positive sample for clenbuterol after the fight, his management company have revealed.
"I would like to assure all fans, the whole of the boxing world and all of Australia that I am not a drug user or a drug cheat," said Browne.
Sydney-born Browne was knocked down in the sixth round but floored Uzbekistan's Chagaev with a big right to improves his record to 24-0.
He added: "I will fight for as long as it takes to clear my name. I have never heard of the drug clenbuterol and had no idea what it is used for.
"I am now aware that it is essentially a weight-stripping drug and as a heavyweight boxer, the idea of me using it is utterly ridiculous.
"My team and I were well aware of the many risks involved in going to a place like Chechnya to fight a reigning champion and believed we had taken sufficient precautions.
"In addition, it was at our insistence that Vada [Voluntary Anti-Doping Association] testing was implemented for the fight."
Clenbuterol is a powerful drug used to treat asthma, but it can also help build up lean muscle mass and burn off fat.
The drug's growth-promoting ability has also found favour with beef farmers, particularly in China and Mexico.
The fact that humans can ingest the substance inadvertently by eating beef has in the past put pressure on anti-doping rules, which deem the slightest trace to be a doping infringement.
WBA heavyweight champion Lucas Browne says he is "shocked and devastated" after failing a drugs test.