Stephen Colbert is replacing David Letterman as CBS’ late-night host. CBS announced Thursday that The Colbert Report host will replace Letterman when he retires next year. Colbert is signed for five years. Letterman has hosted The Late Show With David Letterman since 1993. He turns 67 on Saturday. Comedy Central’s Emmy-winning, The Colbert Report, has been a hit since its launch in 2005.