It's never actually made clear how Yukito found the truth about himself. One moment, Yukito is sitting watching over Touya's sleeping form after Touya collapsed from given Yue his power. The next time they're seen together, Yukito knows about Yue, in fact he is the middle of a full-blown identity crisis, talking about how all his memories have been lies.
"But all the moments we've shared are real."
Touya tells him that nothing has changed for him, that all he wants is to have Yuki by his side. And that's about as much in the way of a confession as we hear from Touya.
As for Yukito... well, that very day Sakura tells him she likes him. When he turns her down she asks if it's because he's already found the person he loves the most. Yukito says yes. And then the ever-clueless Sakura takes her head out of the clouds long enough to ask if that person is her brother. Again, the answer is yes.
Although Yuki tells Sakura that he's not sure what Touya feels from him, from that moment on the two of them begin to act like an established couple. Did Yuki go back and ask Touya? Did Touya do it on his own? Who knows. All that really matters is how things have changed between them by the time they go to the festival at Tsukimine Shrine. The /very/ intimate way they talk to each other alone makes it clear that there are no longer any secrets between them. Then there is the way Touya rests his hand on the back of Yuki's neck as they walk. Or the way he suddenly turns and grabs Yuki's cheeks and tells him teasingly not to worry about what Touya did... or the way Yuki softly touches his own cheek after Touya withdraws his hands.
In truth it's not just they way they relate to each other that has changed. They have too. Touya walks around with a self-satisfied smile, looking very much like a cat that just got into the cream. And Yukito... the oblivious, sometimes hestitant Yuki has disappeared. This Yukito is a lot more sure of himself, he no longer opens wide, amazed eyes as Touya tries to broach difficult subjects, instead he initiates the discussion himself. Come to think of it, he doesn't even act like it's difficult for him to do so in the slightest.
It kind of makes one wonder in what other aspects of their relationship he's willing to take the initiative now. ^.~
The last we see of Touya and Yuki in the anime, they're talking in the Kinomoto's kitchen. Yukito says he's grateful to Clow for creating Yue, because it meant that he, Yukito, got to meet Touya. (And Sakura, but that's really beside the point, ne?)