Tyler confirmed his engagement to Brady on January 2 after weeks of speculation that he popped the question over the holidays.
The rocker has previously professed that he's not a "sexual animal", but revealed on The Ellen DeGeneres Show that he is intensely attracted to Brady.
"The first time I saw her... she worked for Clear Channel so she was paying the band. And I didn't notice her and one night she had on this hair band on around her head. She looked really old-fashion," Tyler told Ellen DeGeneres.
He continued: "So I took her back in the room and she tied me up with it and I thought I'm marrying this girl. Exactly that way."
Tyler also claimed that he's been sober for two years and is committed to living drug-free for the rest of his life.
"I have [a] programme. I got all my friends that are sober now. What it is... It's euphoric recall," he explained. "You hear music and you can get so high and the curtain comes down. It's no different than doing a bump [of drugs]. It's the same thing and that's why it is so dangerous for me. I can't get back into that world."
The singer added: "I can stay high on stage and stay high... I mean out here with you right now my heart's pounding. Hearing [the audience] roar. This is what I live for today. But you never know if it's going to stick.
"I just keep with my programme, wish and hope... I don't want to go back to that place, if that's what you are talking about. That place lost me, my kids, a marriage, a band. A lot of things and it's for real. That's how dangerous that is. So I take it serious."
Tyler, Jennifer Lopez and Randy Jackson return for American Idol's season premiere, which airs over two nights on Wednesday, January 18 and Thursday, January 19 on Fox.
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Watch a clip from Steven Tyler's appearance on The Ellen DeGeneres Show below: