Savion Glover is co-directing Richard LaGravenese's new version of the Rodgers and Hart classic with Tony Goldwyn.
Taymor helmed the original Broadway production of the play, earning a Tony nomination.
The Stage Directors and Choreographers Foundation will present the Bartlett Sher with the award in March.
The latest Simon Rich compendium welcomed a new cast January 20.
The musical, from Victoria and Todd Buchholz, focuses on Bartali's work saving lives in World War II.
Written by Leo McGann and directed by Matt Torney, the Off-Broadway production will stream in February.
Dylan S. Wallach, Abby Goldfarb, and more will star in the David W. Hart play, with Joe Calarco directing.
Joe Murphy will direct the Tony-winning Stephen Sondheim-Hugh Wheeler musical for the U.K. venue.
Voted on by members of the press, the honors recognize the best of Broadway and Off-Broadway.