Letterman, who has been with CBS for 21 years, announced his plans to retire during the April 3 taping of the long-running CBS show at the Ed Sullivan Theatre. The 66-year-old host said he will end his tenure following the end of his current contract, which expires in 2015.
Colbert, a self-professed theatre lover, appeared in the Avery Fisher Hall concert staging of Stephen Sondheim and George Furth's Company in 2011. The production starred Neil Patrick Harris and Patti LuPone.
Colbert's theatre guests have included Stephen Sondheim, Mandy Patinkin and Audra McDonald, as well as James Franco, who first revealed news of his Broadway debut in Of Mice and Men on "The Colbert Report."
A date for Colbert's CBS premiere has not been determined.
