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The unusual arrangement for Diana was made as Broadway remains closed due to the coronavirus pandemic.
"We couldn't be more excited to finally be able to share our show with theatre lovers everywhere," the producers said in a statement on Wednesday.
"Though there is no substitute for the live theatre, we are honoured to be a part of the quality entertainment that Netflix provides its subscribers worldwide."
Diana had been set to open on March 31, 2020, but the debut was delayed as Broadway closed its theatres to help prevent the novel Covid-19 from spreading.
The show had started previews in early March.
The production, which chronicles Diana's courtship and marriage to Prince Charles and eventual divorce, now is scheduled to open on May 25 next year.
The Actors' Equity Association, a labour union representing stage actors, said it had approved a safety plan for rehearsals and recording of the musical.
The plan includes regular Covid testing, isolating actors and stage managers and changes to ventilation in backstage areas, the group said in a statement.