McDonald brings her show Lady Day at Emerson's Bar & Grill, about the jazz singer Billie Holiday, to Wyndham's.
The show won two Tony Awards in 2014, with McDonald scooping best lead actress in a play.
McDonald is the only person to receive Tony awards in all four acting categories. She has won six Tonys in total – more than any other actor.
Lady Day… portrays the troubled life of Billie Holiday, who rose to fame in the 1930s and 40s and died at the age of 44. It will feature several of the singer's classic songs "God Bless the Child", "What a Little Moonlight Can Do," "Strange Fruit" and "Taint Nobody’s Biz-ness."
Ahead of her debut, McDonald will play two concerts in London at Leicester Square Theatre on 17 January.
She will be opening in Broadway show Shuffle Along from 15 March, from which she will take a break to perform in London.
Lady Day at Emerson's Bar & Grill runs at Wyndham's Theatre from 25 June to 3 September.
Watch clips of Lady Day here: