The cast also includes the previously announced Ramin Karimloo, Will Swenson, Caissie Levy, and Nikki M. James.
A glittery performance from the Tony-winning Best Musical will be featured on the telecast.
The romantic tragedy also stars Condola Rashad.
The new concert series will benefit Broadway Cares/Equity Fights AIDS.
You now have an extra week to catch this new "comedic thriller."
The actor was currently on a 12-week medical leave after hurting his shoulder in rehearsal.
According to multiple reports and Tweets by Python Eric Idle, details will be announced at a Thursday press conference.
Bradshaw returns to The New Group with a fresh comedy about racial and sexual tension in an American town.
Nixon's daughter, Persephone Mozes, will also participate.
The high-flying musical will end its run in 2014.