Judy Kuhn, Roger Rees, and more also join the festival's 2014 summer season.
Ambrose and Pine will star in a production of Sam Shepard's Fool for Love.
Rivera will close WTF's 2014 summer season in the revival of Kander and Ebb's The Visit.
The star-studded WTF Late Night Cabaret Series runs through Saturday, January 18.
Broadway's summer home stops in New York for the winter.
The event, which will take place at 54 Below, will also feature Lauren Molina, Todd Almond, and Amy Spanger.
Jenny Gersten will end her tenure with the summer festival this January.
One of the final collaborations between the legendary songwriting pair will join the Williamstown summer season.
The event took place on November 18.
Performers from the award-winning summer theater will offer a winter cabaret series.