The singer, whose hits include You're Still the One and That Don't Impress Me Much, will be a special guest at the event on 10 September.
"I can't wait," she told breakfast show host Chris Evans. "It's been a long time. I'm so excited about it."
Take That top the bill, with Blondie and Rick Astley also playing.
Tickets go on sale this Thursday, 8 June. Full details of how to apply are on the Radio 2 website.
Shania Twain's appearance will be her only UK concert date of 2017, and marks the 20th anniversary of her breakthrough album, Come on Over.
"I'll play a couple of new songs but I will definitely stick primarily to the hits," she said, adding that she wouldn't "wear my top hat" - a reference to her costume in the video for Man! I Feel Like A Woman.
The star spent several years out of the limelight after losing her voice to dysphonia, a condition often associated with psychological trauma.
Her illness followed her divorce from record producer Robert John "Mutt" Lange after he allegedly had an affair with her best friend. However, Twain subsequently attributed the condition to contracting Lyme disease.
Either way, she was unable to sing for several years, requiring extensive physical therapy before she returned to the stage for a Las Vegas residency in 2012.
She is due to release a new album, her first since 2002's Up!, later this year.
Take That headline the festival for a second time, having previously stepped in to replace Lionel Richie, who fell ill days before the event in 2011.
"Do you remember in 2011, when you called me?" frontman Gary Barlow asked Chris Evans, as he recalled the show.
"I think I was at New York Airport and you said, 'Our headliner's let us down, can you come and do it?'
"So I know what this festival's like, brilliant crowds, brilliant atmosphere. So when we were asked by Radio 2, what do you think we were going to say? Yes is the answer, and we cannot wait to be there."
Other acts on the bill include Stereophonics, Seth Lakeman, Emeli Sande and newcomers Wildwood Kin.
Blondie's Debbie Harry said she was looking forward to "bringing everyone together for a huge celebration".
And James Blunt, speaking to Radio 2 "in my dressing gown" from Ibiza, looked forward to playing the Radio 2 festival again, after saying he had the time of his life in previous years.
Last year's event was headlined by Elton John, and included an affectionate tribute to Radio 2 stalwart Sir Terry Wogan.
The festival, established in 2011, is partnered with Radio 3's Proms In The Park, which takes place the preceding day.
That event will be headlined by The Kinks' frontman Ray Davies, with further performances from Bryn Terfel, Gilbert O'Sullivan, Steps and the cast of Five Guys Named Moe.
The evening culminates in a live screening of the Last Night of the Proms, direct from London's Royal Albert Hall.
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Country star Shania Twain will play live in the UK for the first time in 13 years at BBC Radio 2's "festival in a day" in Hyde Park.