David Letterman announced his retirement during Thursday's taping of Late Show With David Letterman, to air at 11:35 p.m. EDT. R.E.M. bassist Mike Mills broke the news via Twitter from the set of the show, as the band is set to appear as Thursday's musical guest. Dave just announced his retirement #2015 #muchlovedave— Mike Mills (@m_millsey) April 3, 2014 News of his upcoming retirement comes seven months after the television host extended his Late Show contract for two more years, though the end of 2015. Letterman has hosted the CBS late night talk show for 20 years -- since August, 1993 -- following his 11-year run as the host of NBC's Late Night.