The 23-year-old announced the news on Twitter and denied reports that a tour of the Disco Inferno musical, in which she had a starring role, was cancelled due to her participation in the BBC contest.
After previously tweeting a "massive apology" to those who had booked tickets for the production, Harmer returned to the social networking site and wrote: "As you know disco inferno has been cancelled but it has nothing to do with me
"It is...All down to bad management and money! But I can now confirm I'm doing strictly come dancing! So yea."
A representative for Harmer said in a statement: "We share the disappointment of Dani's fans that the Disco Inferno tour was regrettably cancelled.
"But we're delighted that the BBC have offered Dani this exciting opportunity, which she is now able to confirm."
A BBC spokesperson added: "We're delighted Dani is on board for Strictly and, when booked, was 100% available."
Harmer has played Tracy Beaker in various BBC adaptations of the Jacqueline Wilson children's book since 2002.
She also reached the final of this year's Let's Dance For Sport Relief after teaming up with Outnumbered star Tyger Drew-Honey for a Bugsy Malone homage.
Strictly Come Dancing will return on Saturday, September 15 at 6.30pm on BBC One.
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