The royal couple also revealed that they would be voting for Girls Aloud star Kimberley Walsh at a charity event at Clarence House yesterday.
Walsh is working with the couple on the search for the UK's 'Diamond Champions', which celebrates older people who give their time to the local community.
Tweeting about the news, the popstar said: "Camilla said she'll vote for me on Strictly! Ha! Right time to get my dancing shoes on!"
The singer had her first full day of training with her pro dancer partner Pasha Kovalev.
"Still smiling at the end of our first day of rehearsal! Dancing is so much fun," said Walsh after her first session.
Strictly's first live shows take place on October 5 and 6 on BBC One.
Photo gallery - Strictly Come Dancing launch show