Daley, 19, said he "couldn't be happier" in the five-minute video in which he speaks about his new partner for the first time.
He added: "I've been dating girls and I've never really had a serious relationship to talk about and now I feel ready to talk about my relationships. Come spring this year my life changed massively when I met someone and it made me feel so happy, so safe, and everything just feels great. And, well, that someone is a guy."
Daley, who won a bronze medal at the London 2012 Olympics, said he wanted to reveal the news in a YouTube video because he didn't want his words to be "twisted".
The Olympics diver said he had only told a handful of people about his relationship including his mother, Debbie, who has been "very supportive".
He added that the rest of his family had had "mixed opinions" since he broke the news to them. "Lots of them didn't believe it. Lots of them wanted me to keep it quiet. Some said: 'Why don't you do a statement?' Some said: 'Why don't you do a magazine cover? Why don't you do a TV interview?'"
"But I didn't want my words twisted. I wanted to put an end to all the rumours, the speculation and just say it and tell you guys because it's what I want to do."
He said in the video: "Most of you are probably wondering why I'm doing this video. My life has been a bit of a rollercoaster, to say the least, over the last couple of years. Losing my dad to cancer in 2011 was the one of the hardest things I've ever had to deal with in my life. Winning an Olympic medal last year in 2012 in front of a home crowd. Finishing my A-levels this year. I mean, it's been hectic.
"One thing that I consider pretty important is to have some form of private life. You're probably thinking: 'Why did you do a book? Why did you do a documentary and all that kind of stuff?' I've only ever talked about things that I feel comfortable talking about. When I was younger I hated talking about the bullying situation at school. I didn't like talking about my dad because obviously at the time it was a sensitive subject but it's one of those things.
"In an ideal world I wouldn't be doing this video because it shouldn't matter. But recently I was misquoted in an interview and it made me feel really angry and frustrated and emotions that I've never felt before when reading anything about myself. For me honesty is something I really do believe in. I've always been honest. I may have been vague in some of my answers but I've always been honest. One thing I've never felt that comfortable talking about are my relationships. It's what I get asked, even if I'm doing sporting interviews, it's: 'Do you have a girlfriend? Who are you seeing?' All that kind of stuff. I've been dating girls and I've never really had a serious relationship to talk about and now I feel ready to talk about my relationships. Come spring this year my life changed massively when I met someone and it made me feel so happy, so safe, and everything just feels great. And, well, that someone is a guy. And it did take me by surprise a little bit. It was always in the back of my head that something like that could happen but it wasn't until spring this year that something just clicked. It felt right. Like I said, my whole world just changed there and then. Of course I still fancy girls but, I mean, right now I'm dating a guy and I couldn't be happier. It feels safe and it really does feel right.
"People are going to have their opinions and people are going to make a big deal of it. Is it a big deal? I don't think so. People will call me a liar and … I mean, it's going to be big but I wanted to say something and I feel like now I'm ready and wanted to do it. People will think: 'What would your dad have said?' and he always said to me: 'As long as you're happy, I'm happy,' and right now I couldn't be happier. My mum's been very supportive as well. I can count the number of people I've told on my hand but all my friends and family I've told have been so supportive which has been great. But I told the rest of my family today and, well, let's just say they had mixed opinions. Lots of them didn't believe it. Lots of them wanted me to keep it quiet. Some said: 'Why don't you do a statement?' Some said: 'Why don't you do a magazine cover? Why don't you do a TV interview?' But I didn't want my words twisted.
"I wanted to put an end to all the rumours, the speculation and just say it and tell you guys because it's what I want to do. My friends and family are always there to support me and I hope you guys can be too. I'm still Tom. I still want to win an Olympic medal in Rio 2016 for Great Britain. I'm still as motivated as ever to do that and it would be great to have you guys on that journey as well. I just wanted to make sure I tell you guys before I head off to Houston for a training camp that I've got up until Christmas. So I'm glad I've got it off my chest and I hope you can join me on the journey to Rio 2016 too."
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