Brian Eno told the London Times how he and Byrne got together for their first album since 1981's seminal My Life in the Bush of Ghosts. He said: "I bumped into David in New York. We had dinner together and I happened to say I had a lot of music I had intended to turn into songs, but hadn't got round to. He said: 'Oh, I've got a few lyrics.' It was as simple as that."

This was the first fruit from their collaboration after Eno had sent Byrne some instrumental tracks on a CD. Byrne wrote on his website the story of this song: "I attacked the first one, which I think was called 'And Suddenly' on Brian's track list. I'd just finished reading Dave Eggers book What is the What?, about Valentine and his hallucinatory and horrific journey as a very young man that took him from his destroyed village in Darfur to Atlanta Georgia and beyond. Valentine's story was harrowing but also beautiful, uplifting (in a non corny way) and at times even funny. I think I might have still been under the influence of his story when I sat down in front of my microphone. The result became 'One Fine Day.' I sang a few harmonies in the choruses to make it sound better and send it off to Brian. We were both thrilled- here was the gospel-folk-electronic aspect I at least had heard hints of had come to life- articulated. The words had some Biblical allusions, but nothing too overt. We agreed to continue, for now."

Eno revealed to Rolling Stone magazine that Coldplay's Chris Martin came close to collaborating with him on this rather than Byrne. Eno explained that he played a piece of instrumental music in his London studio for Martin: "Chris said, 'Wow, I'd love to work on that.' I'd given it to David a few months before and hadn't heard anything back. So I gave it to Chris."
Six months later, on the same day that Martin told Eno he had written "the most amazing song" for that track, Byrne finally e-mailed him an MP3 of this song. The Art Rock legend told Rolling Stone that Martin responded by saying "I can't do better than that." Eno added with a chuckle, "Incredible timing."