Mackintosh and Disney partnered for the project after the veteran producer secured the stage rights to Pamela Travers' book, the Western Mail reported Friday.
The stage version will be similar to the film, which starred Dick Van Dyke and Julie Andrews, "but which has its own life, which is what one always strives for with any adaptation of anything," Mackintosh said.
"That means you can expect 'A Spoonful Of Sugar' and 'Chim Chim Cher-ee' and a few surprises," he said, adding a new song "Practically Perfect" will be used to introduce Mary Poppins.
The producer selected a relative newcomer in the title role, Laura Michelle Kelly.
Kelly, who won Cardiff, England's, first Voice of Musical Theater contest, followed Martine McCutcheon in "My Fair Lady."
"I wanted to pick someone to play Mary who could make the role her own and who wouldn't come with much baggage," Mackintosh said.