Urban recently worked with Swift on the song "That's When." The track appears on Fearless (Taylor's Version), a rerecorded version of Swift's 2008 album Fearless, released this month.
On Ellen, Urban said he was Christmas shopping at a mall in Australia in December when Swift texted him about collaborating.
"So I'm at the shopping mall doing my Christmas shopping and I get a text from Taylor saying, 'I've got these couple of songs I'd like you to sing on. Do you want to hear them?'" Urban recalled.
"I'm sitting in the food court at the shopping center, listening to these two unreleased Taylor Swift songs," he added. "It was an unusual place to be hearing unreleased Taylor Swift songs. But I loved the songs, and luckily got to put a vocal on both of those."
"She just had that ... there's this thing where people are playing into the future. When they play a show you can just tell that their eyes are set way, way ahead of where they're going -- where they are. She had that right from the beginning," Urban said.
"I think truly for me, I think she's one of our generation's great, great songwriters, period," he added.