CBS announced that the long-running talk show would be celebrated with three-night episodes.
Hanks will feature on Monday, May 18. It will mark his 60th appearance on the show. Vedder will perform on the same day, backed by Paul Shaffer and the CBS Orchestra.
Murray will appear on Tuesday, May 19. He will make his 44th appearance with Letterman.
He was the very first guest in the first episode of Letterman's "Late Night" on NBC on February 1, 1982. Murray was the only name announced for the Tuesday episode, leaving many possible names to appear that day.
By the time he retires, the 68-year-old veteran comedian will have hosted 6,028 late-night talk show broadcasts over 33 years, accumulating his tenure on NBC's "Late Night" and CBS' "Late Show".
He has spent more than 21 years hosting "Late Show with David Letterman" and won Outstanding Variety, Music or Comedy Series award six times.