The program, which airs on PBS in May, is a revue of milestone Broadway shows from 1973 to 2023.
Rice is the first songwriter primarily known for his work in theater to receive this award since Stephen Sondheim in 1999.
The production will open on March 16 at Bernard B. Jacobs Theatre following its sold-out New York City Center run.
The revival brought in just above $2 million across eight shows last week, a record for August Wilson Theatre.
Onstage and onscreen, the composer of the new Almost Famous musical usually juggles multiple projects — and roles — at once.