The 29-year-old, an Austrian drag queen who found global fame after winning the competition in 2014 with the song Rise Like a Phoenix, informed fans of her diagnosis on Instagram, stating that she had chose to go public after an ex-boyfriend threatened to do so.
Wurst said her treatment for HIV, which is spread when infected fluid enters the bloodstream, was going well.
"I won't give anyone the right to scare me and to influence my life in this way, ' said Wurst, describing the decision to go public as removing a 'sword of Damocles".
She praised the "unconditional support" she had received from her family and added that sparing them the publicity was one reason she had not chosen to share the information before now.
"I would have gladly spared you the attention of the HIV status of your son, grandson and brother".
"Coming out is better than being outed by a third party".
"Likewise, my friends have been aware of this for quite some time and are dealing with it in the non-judgemental way that I would hope everyone else will".
"To my fans: the information about my HIV status may be new but my status is not!"
She thanked fans for their support, and said she feels "stronger, more motivated and liberated than ever".
"Threatening to reveal someone's HIV status, under any circumstances, is entirely wrong".
Wurst revealed that regular treatment had suppressed the virus.
"I have to put a stop to this onslaught, this barrage of attacks and of sub-truths and very harmful and mercurial stories that are about me, threatening the health of so many others, which couldn't be further from the truth".
Born Tom Neuwirth in Styria, Austria, Conchita became an worldwide sensation when she won Eurovision in with Rise Like A Phoenix. And we know this isn't something which only happens to those in the public eye. H.I.V. can be treated with drugs that reduce the viral load to a level where the immune system is healthy and the patient cannot pass on the virus.