Steve Reich, the baseball-capped titan of modern music, is in a laconic mood this early New York morning, not to say clipped and to the point.

Asked what he expects to find in Glasgow from March 9, when he will stay in the city for the first time, performing new and old music from his glittering career, he replies: "An audience. Some music. Some loud speakers."

Down the telephone line, one can hear nothing but transatlantic static and the bustling streets of his home town coming to life. Interviews have started more smoothly.

Luckily, we both have talk of Radiohead to break the silence. The centrepiece of Reich's visit to Glasgow is the world premiere of a new work, his 20-minute long Radio Rewrite, a new commission based on songs by Radiohead, performed by what he calls a "national treasure", the London Sinfonietta.

Reich, born in 1936, became acquainted with the Oxford band when he was in Krakow, Poland, at a festival of his music. One of the performers there was the classically trained Radiohead guitarist Jonny Greenwood. Greenwood, as well as being the man who provided the hit-making crunch on Creep and played ondes Martenot on OK Computer, studied music at Oxford Brookes University, and is now gathering a reputation as an orchestral composer, particularly of soundtracks to films such as There Will Be Blood and The Master.

In Krakow, Greenwood performed Reich's blissful cataract of recorded and live sound, Electric Counterpoint, having prepared the backing tracks himself. Reich was struck by the talent and background of the younger musician. "It was a great performance and we began talking," he says. "I found his background as a violist and his present active role as a composer extremely interesting when added to his major role in such an important and innovative rock group. Festival director Filip Berkowitz suggested I listen to Radiohead. When I returned home I made it a point to go online and listen to their music and two songs stuck in my head. It was not my intention to make anything like variations on these songs, but rather to draw on their harmonies and sometimes melodic fragments and work them into my own piece."

The two songs he took to form the spine of his new work were the plangent Everything in Its Right Place, from 2000's Kid A, and Jigsaw Falling Into Place from 2007's In Rainbows. Asked what struck him about these songs, Reich is more loquacious. "They attracted me immediately. I think with Everything ... it was something about that melody, with that opening series of chords being one of the classics in Western music. For Jigsaw, it's the harmonic jumps of the piece, it's a beautiful tune. And in my piece, there are moments where you will recognise melody from those two songs, and lots of times where they doesn't appear to be any of them in it at all."

He adds: "Everything is a very rich song. It's very simple and very complex at the same time. What does it mean? Maybe it's about a relationship, maybe I should ask Thom Yorke [Radiohead singer/songwriter] but he wouldn't tell me, I wouldn't get anywhere with that."

Usually, Reich's work inspires rock and dance bands, rather than the other way around. His work has been sampled by electronic acts (The Orb, Coldcut, DJ Spooky) and, with seminal works such as the still majestic Music for 18 Musicians, released in 1978, influenced many more. Taking on the sounds of a guitar band, even one as sophisticated as Radiohead, is a new move.

"It's just music," he says. "I was interested in Jonny, I knew he had been classically trained. I had heard the music for There Will Be Blood, but I never would have thought the composer would have anything to do with a rock'n'roll band. We met, we talked and we hit if off. It seemed he was interested in my music and I was interested in his. When I listened to the music, those two songs just emerged as my favourites, they just started to get my juices flowing.

"I had been working on another piece at the time, and it was a real dog, it was taking a long time. The Radiohead music was more interesting and energising – there are people who can read music and there are musicians who play rock'n'roll and I see no problem with that at all."

After all, he says, composers have long worked with pre-existing material for new pieces, often with folk music in the past. He mentions the song L'Homme Arme as the basis for a Mass and Stravinsky reworking Pergolesi for his own composition. In the new piece there are five movements, played without pause. The first, third and fifth movements are fast and based on Jigsaw and the second and fourth are slow and based on Everything. The piece is scored for flute, clarinet, two vibes, two pianos, a string quartet and an electric bass. Is this something Reich might consider working with again, the rough and tumble of contemporary guitar music? "No. I try not to repeat myself. And I know that sounds funny because I am so famous, I suppose, for repetition. But I try not to do the same thing twice."

As well as Radio Rewrite, the two-day celebration of Reich's music will also include a performance of Clapping Music by the composer, as well as Electric Counterpoint, 2 x 5 and Double Sextet, culminating in the Colin Currie Group's performance of Drumming. The composer said he will be staying in a "very different" hotel to the one when he was in Scotland last. It was a British Council tour, he thinks, in the late 1970s and he was put in a bed and breakfast in Aberdeen so cold and rickety that when he tried to turn the heater on, he feared he would burn down the curtains.

"I will still be working, I think you always have to work," he says of the upcoming trip. "I work most days. I take my laptop and work on that when I am away. Of course, life has its errands, but if you sit and wait around for inspiration you will be dead before it strikes."

Steve Reich is in Glasgow on March 9 and 10 at the city's Royal Concert Hall.