The Olympian came out on Monday in a video posted to YouTube, telling fans that he wanted to "put an end to all the rumors" about his sexuality.
Daley, who won the bronze for England at last year's Summer Olympics, said, "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."
That guy is Black, according to Britain's The Sun newspaper.
"He's besotted with Dustin. They love each other and aren't concerned what anyone says about age difference (Black is 20 years older than Daley)," a source told The Sun.
"Dustin is very proud of Tom for making such a powerful statement about his sexuality - it's what he believes in doing," the source adds. "Dustin has given Tom the confidence to be himself. He's in awe of him and proud of him. He no longer minds people knowing they are together."
Black won an Oscar in 2009 for writing the screenplay for "Milk."