Scott Rudin will produce the production, with Jack O'Brien directing a cast that also includes John Goodman, said The Hollywood Reporter.
Lane, 60, will play tabloid editor Walter Burns, with 53-year-old "Spotlight" actor Slattery as his star reporter Hildy Johnson in the production.
The original play, by Ben Hecht and Charles MacArthur, was inspired by their years as Chicago journalists.
It takes place entirely in the press room of Chicago's Criminal Courts Building, where hacks from various city papers play poker and swap wisecracks while waiting to cover a big case that takes an unexpected turn.
The production is slated for a limited engagement of around five months, with performances starting in September and an official opening planned for October 20 at a theatre to be announced.
The play ran for 276 performances in its Broadway premiere and has been revived three times since, most recently with John Lithgow and Richard Thomas in 1986.