The music legend honoured one of his most famous fans by singing 'The Night We Called It a Day' on the episode.
The 73-year-old musician - who is rarely seen on TV - returned to the show for the first time in over 20 years and gave a moving rendition of Frank Sinatra's classic song, from his latest album 'Shadows in the Night'.
In a display of gratitude to Dylan whose last appearance was back in 1993, Letterman revealed two pieces of life advice he gave to his son, one of which involved the folk singer.
Recalling what he said to his child, Letterman said: ''You have to be nice to other people and the greatest song writer of modern times is Bob Dylan.''
As the credits rolled, Dylan remained silent and simply shook Letterman's hand, while the host responded by saying: ''Beautiful, thanks Bob. Beautiful''.
Bill Murray was a guest on the show and when the curtain opened to introduce the comedic actor, he stumbled and tripped out of a giant-sized cake and hugged the host, leaving him covered in icing.
Murray - who was Letterman's first ever guest - then ran around the studio and high fived members of the audience and the house band.
For previous appearances, Murray has entered as Peter Pan, a dumpster diver, Liberace, a marathon runner and in just a tux after apparently water-skiing at George Clooney's wedding.
The final ever episode of 'The David Letterman Show' will air tonight (20.05.15).
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