The store will feature exclusive merchandise and experiences for Broadway fans.
The Broadway veteran and philanthropist will accept the honor at this year's Tony Awards ceremony.
The event will be broadcast live from New York's Diamond Horseshoe at the Paramount Hotel.
The Tony Awards Administration Committee has announced its latest decisions.
The annual broadcast, honoring the best of Broadway, airs June 8.
Weiss has won the award four times for his direction of past Tony Awards broadcasts.
Among other rulings, Billy Crudup and Shuler Hensley will be considered eligible for their roles in both Waiting for Godot and No Man's Land.
Because you're clearly showing off when you've won five Tony Awards.