To celebrate the 100th birthday of his beloved Judy Garland, Rufus Wainwright went over the top — or better yet, over the rainbow — with his centenary gift: It’s an entire new album, “Rufus Does Judy at Capitol Studios,” that dropped on Friday — exactly 100 years after his iconic idol was born on June 10, 1922.

It’s the second Garland tribute LP by the 48-year-old art-pop artist, after 2007’s “Rufus Does Judy at Carnegie Hall.” And also on Friday, he’ll fête the Hollywood legend — who died on June 22, 1969 — with the last night of this week’s “Rufus Does Judy at City Winery” residency in Chelsea.

Here, Wainwright shares how he discovered Garland, what she means to him as a gay man, and why Pride Month is the perfect time to honor her.

Obviously Judy Garland has meant so much to you throughout your life. How did you first get exposed to Judy?

Well, “The Wizard of Oz” was a kind of yearly TV event that would occur around Easter usually. So the whole family would watch it. It started then, and then I sort of followed her entertainment yellow brick road. When I got to Hollywood and I saw her history — and also sort of the lore of the gay world — those things just kind of haunted me for many, many years.

Why do you think she has been the ultimate gay icon, that she has been so special to the gay community?

I think that she experienced a lot of the same traumas that a lot of gay men experience, whether it’s through battles with addiction or feeling really taken advantage of by society — or not respected, shall we say. Sometimes gay men, especially from that generation, were not allowed to express themselves, so there’s that kind of trapped feeling … And I think that a lot of gay men feel like there’s this inner Judy who wants to be known for who they are.

There’s also this connection between Judy and Stonewall, because she died right before the Stonewall Riots in 1969.

I was honored to be able to sing “Over the Rainbow” on Tuesday at Stonewall, where they unveiled this beautiful portrait of her that will be a permanent fixture of that space. It meant a lot to me as someone who’s been gay their whole life and also really known about Judy Garland their whole life.

There was “Over the Rainbow,” and then the rainbow became the symbol of the gay movement.

Yeah, I think it memorializes it. It very much kind of adds to the strength that, sadly, the gay community needs.

A gay man used to be called “a friend of Dorothy,” of course referencing her “Wizard of Oz” character. But it’s pretty incredible that she has remained in the fabric of the gay community for all these years, for generations really.

What’s nice about it is that at the end of the day — in spite of all of the symbolism and dramatic stories and so forth attached to her — in the end, it’s all connected to the fact that she was an incredible singer and a great musician. And anyone — be it gay, straight, bisexual or transgender — can listen to those records and be moved by them. And that’s the most important thing.

In your City Winery show on Tuesday night, you talked about the fact that when you did “Rufus Does Judy at Carnegie Hall,” you really connected with Judy in a different way because of things that you were going through.

When I first did the concert many years ago, in a lot of ways it was to exorcise Judy from me. I was a little bit overly obsessed with her. And certainly in my trials and tribulations with drugs and alcohol, I was fighting this kind of Judy-esque demon in a way. It was a way of maybe letting Judy go for a little while and maybe even setting her free … But years later now, I’m a little older, and I’ve been around for a while, and I’ve certainly survived Hollywood. Now she’s back, and it’s more about her positive aspects and more about her strengths and her kind of resilience that I’m more attracted to at the moment.

When you recorded this new album, you even used the microphone that she once used, right?

Yeah, I did. I used her mic, and I recorded at Capitol Studios [in Hollywood] where she made a lot of records. It’s more of a kind of jazz record, which I never really expected to make. It’s with these really wonderful players who are really good at getting into the minutiae of the music, and so we were able to do that in that incredible room.

As we remember Judy and honor her on her 100th birthday, is there anything about her that you think is underappreciated?

Well, she was one of the great actresses too. Her sense of timing was impeccable in terms of acting. And it’s a pity that she never did anything on stage, in the sense that she was never in a Broadway show. I think that would have been an amazing turn of events.

What’s the Judy Garland song that speaks to you in the most personal way?

Well, I mean, at the end of the day one has to go with “Over the Rainbow.” I would say it’s probably the best song ever written. It’s the kind of song that, when you sing it, you have to become invested emotionally in it. You can’t just toss it off. You gotta go there.

If you had gotten to meet Judy, what would you have liked to say to her?

Oh, I don’t know … Wanna go to an AA meeting with me? [Laughs.]