The big concert went on sale via SeeTickets at 8am this morning but fans faced difficulty making their purchases as the site struggled to cope with demand.
The show takes place on September 10 and also boasts Take That, Blondie and James Blunt.
Emeli Sande, Rick Astley and Stereophonics will also perform.
The show is Twain’s only UK show of 2017 and comes amid her long-awaited comeback.
She had tweeted yesterday: “I’m playing this year’s @BBCRadio2 Live In Hyde Park!
“Tickets on sale 8am tomorrow, can’t wait to play for you London! #R2HydePark.”
The superstar had previously claimed her 2015 Rock This Country tour of North America would be her last time on the road, but she soon U-turned and announced a comeback.
“This is my last tour, so I’m going to make the most of it. I want to go out with a bang,” she told Rolling Stone at the time.
Her new single Life’s About To Get Good is expected for release very soon.
She has sold over 85 million records across her career.
BBC Radio 2 Live in Hyde Park takes place on September 10.