In an interview with the Sunday Mirror, the 52-year-old said she was both nervous and excited about coming out.
"I needed to do this now, for me. It was my decision. I'm nervous about saying it. I feel like I'm going to explode with excitement," she said.
"Sometimes I cry with relief. The moment this comes out, I'm essentially getting rid of that fear."
Dame Kelly became only the third woman in history and the first Briton since Albert Hill 84 years earlier to win the 800m and 1500m Olympic double at the Athens games in 2004.
She has achieved seven gold, eight silver and four bronze Olympic, Commonwealth and European medals throughout her athletic career.
She shared the news during Pride month, which celebrates and raises awareness about LGBTQ+ communities and will this year commemorate 50 years since the UK's first Pride march.
Writing on Instagram as the interview was published online, Dame Kelly said: "I can finally breathe.
"Yes I have been petrified of putting this out - you have no idea.
"This journey has been the hardest part of life. Living with any kind of fear is debilitating".
Several celebrities posted supportive comments, including comedian Alan Carr, professional dancer Oti Mabuse, music producer Naughty Boy, and drag queen Baga Chipz.
Dame Kelly said she had also filmed a documentary for ITV about helping people "live their authentic lives" - it airs later this month.
In her interview with the Mirror, Dame Kelly spoke of her concern that she would be punished for being gay and serving in the Army.
"I was convinced throughout my whole life that if I admitted to being gay in the Army I'd still be in trouble," she said.
She described an incident where the Royal Military Police searched her accommodation in what she believed to be an attempt to uncover her sexuality.
"They pulled everything out of your cupboard, turned out the beds and drawers, read letters - everything - trying to catch us out, so we could be arrested, court martialled and potentially go to jail," she said.
Dame Kelly left professional running at 18 to join the Army in the late 1980s, becoming an HGV driver and a physical training instructor.
She was awarded an MBE for services to the Army in 1998, and in 2018, she became the first person to be appointed Honorary Colonel to a regular unit, the Royal Armoured Corps.
Gay, transgender and bisexual people in the military faced prison if their sexuality or gender identity was discovered.
The law was changed in 2000 after four servicemen and women, who were sacked for being gay, won a case in the European Court of Human Rights.