The star, real-name Louisa Rose Allen, will perform a track in the new series which stars Peter Capaldi as the latest regeneration of the timelord.
She said: "I can't believe I'm actually going to be in an episode of Doctor Who! Especially as it all came about from a chance meeting.
"I was playing a gig and got chatting to the show's production team who'd been watching my performance. I was telling them how much I loved Doctor Who and next thing they invited me to be on it.
"I couldn't think of a better place to make my acting debut than on one of the UK's most iconic shows."
The Grammy award winner is just finishing her UK tour in support of her new album, Glorious.
She is one of several guest stars appearing in the new series including Frank Skinner, Ben Miller, Tom Riley, Keeley Hawes and Hermione Norris.
Show supremo Steven Moffat said: "We are completely thrilled that the amazingly talented Foxes is joining us on board ... Well, you'll see.
"Let's just say, the Doctor is finally catching up on his phone calls."