It will be the first time the show has been seen in central London since 1990.
Set in Depression-era New York, it tells of a young performer, Peggy Sawyer, who gets a shot at stardom when her show's leading lady is injured.
The new production begins previews on 20 March and will be directed by the original show's co-author Mark Bramble.
First staged on Broadway in 1980, 42nd Street was named best musical at the following year's Tony Awards.
Its original London production, whose cast included a young Catherine Zeta-Jones, won the Olivier award for best musical in 1984.
Zeta-Jones was a second understudy on the production who got a chance to perform when both leading lady Barbara King and her first understudy were indisposed.
A Broadway revival in 2001 brought further accolades, including a Tony for musical revival.
The show has since been seen at various UK venues, among them the Chichester Festival Theatre in 2010.
"The original production had the look of a Warner Brothers black-and-white film," said Bramble.
"This time we're doing an MGM Technicolor version of 42nd Street with additional songs and dances.
"The theme of the show speaks louder today than ever before: Follow your bliss and with talent and hard work dreams can come true."
Ruby Keeler played Peggy in the original film, best-known for the scene in which she is told: "You're going out a youngster but you've got to come back a star!"
42nd Street will open at the Theatre Royal Drury Lane, currently home to the musical version of Charlie and the Chocolate Factory.
Casting for the show, which will have its official opening night on 4 April 2017, will be announced at a later date.
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The stage version of classic film 42nd Street will return to the West End next year, with its producers promising even more singing and dancing than before.