The comedian, known for his sardonic wit, announced his retirement in April. CBS has not said when Colbert, the host of Comedy Central's faux political news show "The Colbert Report," will begin as "Late Show" host.
Colbert's final broadcast of "The Colbert Report" is scheduled to air on Dec. 18.
Letterman, 67, began his late night career as the host of NBC's "Late Night" in 1982. He left that network in 1993 after losing out to Jay Leno to be the host of NBC's "Tonight Show."
Letterman's retirement marks the end of a generational shift in the late night TV landscape as networks look to attract younger audiences.