Who is replacing David Letterman? Fri-11-Apr-14 09:16 Share this By Jay-Jay FeeneyDavid Letterman is retiring from The Late Show next year and his replacement has been announced. Stephen Colbert will succeed David Letterman. Stephen has been the host of Comedy Central's "The Colbert Report" since 2005. You May Also Like David Letterman grills Lindsay Lohan about her drug and alcohol problems Lady Gaga spends quality time with her fans Amanda Seyfried drunk in interview Become a fan of The Edge on Facebook and on Twitter .