CBS is expected to issue a statement sometime before the program is broadcast Thursday night.
Letterman's announcement initially leaked out when a performer, Mike Mills, who was at the taping of "The Late Show" tweeted out the news. "Dave just announced his retirement," Mills wrote.
Letterman, 66, launched the late night show in 1993 at the Ed Sullivan Theater in New York City. Known for his wit and acerbic asides, Letterman has hosted the show without many interruptions, saved for his bypass surgery in 2000.