DAVID LETTERMAN announced that he's retiring next year on "The Late Show" last night. 


Dave began by talking about how he will turn 67 on April 12th . . . and how he's been hosting a late night show since he was 34.  He explained that he's done 4,014 shows on CBS, after doing 1,810 shows on NBC.


He went on for a few minutes, before saying that earlier in the day, he called the owner of CBS and let him know that he's RETIRING.  That's when PAUL SHAFFER joked, quote, "You actually did this?  Do I have a minute to call my accountant?"


David joked, quote. "What this means now, is that Paul and I can be married."


There's no timetable for his last day yet.  David just said, quote, "It'll be, I think, at least a year or so, but sometime in the not too distant future.  [In] 2015 for the love of God, in fact, Paul and I will be wrapping things up and taking a hike."