The five-time Olympic gold medallist makes the revelation in an interview with British presenter Michael Parkinson due to be aired later Sunday by Australia's Channel Ten, reports said.
Australia's Sunday Telegraph newspaper said the 31-year-old also describes his years of battling with depression in the emotional interview recorded last month.
His decision to come out as gay attracted a flurry of supportive comments.
Fellow Olympic swimmer Stephanie Rice tweeted: "Thorpie is and always will be a superstar in my eyes."
Another tweeter said: "I'm sad that there are people - not just great sportspeople - who feel they have to hide who they are every day. I hope Thorpie feels free."
Olympic diver Matthew Mitcham, who revealed he was gay in 2008, said he could "totally understand how difficult this whole process has been for him".
"I really hope this process gives him some peace and that the media and the public give him the same respect and the same overwhelming support I received in 2008," he told the Telegraph.
- 'Huge personal cost' -
Australian Marriage Equality national director Rodney Croome praised Thorpe for coming out.
"(It) has clearly been a difficult struggle for him and I hope Australians appreciate the trust and confidence he has placed in us all by revealing he is gay," Croome said.
"Nothing has changed about Ian Thorpe. He is still a great Olympian and a great Australian," he added.
The Gay and Lesbian International Sports Association also paid tribute to Thorpe, acknowledging the "psychological pain" he endured while keeping his sexuality a secret.
"For whatever his reasons, which must be respected, he felt unable to be open about his sexuality during the height of his sporting career, which has come at a huge personal cost," president Barry Taylor said in a statement.
The swimmer -- known by his nickname "Thorpedo" -- retired in 2006 after a glittering career in which he ruled the pool from 1998 to 2004, taking nine Olympic medals and 11 world titles and setting 13 long course world records.
He returned to racing in 2011 but had a string of disappointing results leading up to his ultimately unsuccessful London Olympic bid the following year.
Since calling it quits for a second time in 2013, Thorpe has endured several health setbacks.
In February he began treatment for depression after a mixture of painkillers and anti-depressants left him disoriented on a Sydney street.
He was hospitalised for more than three weeks in April after battling serious infections for shoulder surgery. At one point there were rumours he would lose the use of his left arm, although they proved unfounded.
Previously, Thorpe strongly denied rumours of his homosexuality.
In his 2012 autobiography "This Is Me", the swimmer wrote: "For the record, I am not gay and all my sexual experiences have been straight. I'm attracted to women, I love children and aspire to have a family one day."
He added: "I know what it's like to grow up and be told what your sexuality is, then realising that it's not the full reality. I was accused of being gay before I knew who I was."