Jamie Parker, currently starring in the West End show Guys and Dolls, will star as an adult Harry in the production, set 19 years after JK Rowling’s books.
Noma Dumezweni, who recently stepped in at the last minute to replace Kim Cattrall in Linda at the Royal Court, will play Hermione Granger.
London Road star Paul Thornley completes the trio as Ron Weasley.
“I’m so excited with the choice of casting for Harry Potter and the Cursed Child,” Rowling said.
“I can’t wait to see Jamie, Noma and Paul bring the adult Harry, Hermione and Ron to life on stage next summer.”
Jack Thorne’s two-part play – based on an original new story by Rowling, Thorne and director John Tiffany – sees Harry as both a father of three school-age children and an overworked employee of the Ministry of Magic.
“While Harry grapples with a past that refuses to stay where it belongs, his youngest son Albus must struggle with the weight of a family legacy he never wanted,” said producers.
Parker’s other stage credits include being an original member of Alan Bennett’s The History Boys at the National Theatre – a role he reprised on the big screen in 2006.
Dumezweni won a best supporting actress Olivier award in 2005 for her role in A Raisin in the Sun.
The South African-born actress also starred alongside Chiwetel Ejiofor and Audrey Tautou in 2002 film Dirty Pretty Things.
Stage regular Thornley recently featured in Simon Pegg’s romantic comedy Man Up and also appeared in ITV drama Life Begins opposite Caroline Quentin.
Previews of Harry Potter and the Cursed Child begin on 7 June at the Palace Theatre, with both plays set to open on 30 July.