The Chicago-born star told Chris Evans on his BBC Radio 2 Breakfast Show "the seed was planted" to take part when she sang on the show last year.
Despite admitting she could not dance, the singer said was "game" to take part, but had done "absolutely nothing" to prepare.
The new series begins in September.
Olly Murs and Rebecca Ferguson are to perform on the launch show, broadcast on 3 September, it has been confirmed.
The 15 celebrity contestants will find out on the show which professional dancer they have been matched with.
When she was asked if she wanted to appear on Strictly as a contestant, Anastacia said she replied: "I'd stink - do you really want me on the show?"
"I'm serious," the 47-year-old told Evans. "I'm not lying about it at all. I just finished 62 dates on tour so I'm really good at rhythm and sidestepping - as far as to my own music. Butâ€¦ uh oh."
When Evans said it was "fantastic" the singer would be on Strictly, she replied: "You say it's fantastic now - you haven't seen me dance yet."
The singer said she had a "slew of health issues" - including Crohn's disease, breast cancer and a heart condition - joking: "I'm ticking them off, honey."
She added of the dancing series: "I did it because I wanted to challenge myself on something that had nothing to do with a hospital."
Speaking on the Strictly website, the singer said: "After my double mastectomy, it stripped away a part of me that I feel I would like to find again.
"This opportunity has come at a perfect time to help me use and get to know my upper body again."
She added she was most looking forward to dancing the Salsa because she thinks she has "a 28-year-old Latina trapped inside" her body.
Anastacia shot to international fame in 2000 with her debut song I'm Outta Love, which she performed on the Strictly Blackpool special last year.
BBC Breakfast's Naga Munchetty, politician Ed Balls, model Daisy Lowe, former Hollyoaks actor Danny Mac, Kiss FM DJ Melvin Odoom, singers Louise Redknapp and Will Young; and presenters Ore Oduba and Laura Whitmore are the other confirmed celebrity contestants on the show.
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US singer Anastacia says she "can't wait to get started" as she was announced as the 10th contestant for Strictly Come Dancing.