The two divorcees fell in love while working on Hopeless Romantic, Branch's first new album in 14 years, and Carney made his first non-The Black Keys appearance when he joined his girlfriend onstage at New York’s Bowery Electric for a showcase gig in January (17).

"This record wouldn’t have seen the light of day had he not been involved," the 33-year-old tells Billboard, "That’s why it was important for him to be up there. When we were making it, it felt like it was us against the world."

Carney signed on to produce Hopeless Romantic just after Branch finalised her divorce from musician Teddy Landau, and singer and producer quickly became an item in the studio.

"We started realising that we were completely falling in love," she says, revealing she recently moved from Los Angeles to Nashville to live with Carney, and she admits she wishes the couple had met years ago.

"Pat has said, 'I ­remember seeing you on MTV in the early 2000s and ­thinking you were really cute'," Michelle adds. "It's like, why couldn't we have just met each other in our 20s? We would have saved so much heartache! He said that we probably would have f**ked it up. And yeah, we ­probably would have."

Carney has two failed marriages behind him and Branch split from Landau, the father of her 11-year-old daughter, in 2014, just before meeting the Black Keys star at a party in Los Angeles.

They teamed up after Michelle was given money to record a four-track sampler by Verve CEO David Foster, but the music mogul wasn't a fan of what he heard: "He said the guitar was too aggressive, I didn't sound like myself - that I was making a huge mistake," Branch recalls to Billboard. Carney came to her rescue and offered to ­personally finance the album.

Foster was replaced by Tony Bennett's son Danny by the time the album was complete and he had a very different take on Branch's collaboration with her new man: "He listened to it, called me and said, 'I love this album. Don't change a thing!'"

The new couple will now put the romance to the test on the road, when Carney joins his girlfriend as her touring drummer.