This is a slight reinterpretation of dQQm's tab on UG in addition to 
Mahayana's tab here: http://jazzguitar.proboards.com/index.cgi?board=comping&
action=display&thread=419&page=1.

Chords (remember to swing 'em!):

Bb (x 1 3 3 3 1)
Cm (x 3 5 5 4 3)
Cm7(x 3 5 3 4 3)
Gm (3 5 5 3 3 3), although I like playing it without the root
F#7 (2 4 2 3 3 3), although I often skip the top two strings
F7 (1 3 1 2 1 1) OR (x 3 3 2 4 x) This second chord probably isn't F7 for
all I know, but it allows you to to throw in one of these (x 3 3 0 x x)after
it.

I chose these chord shapes because they are easy to move. Starting with the
third verse (and throughout the rest of the song), each verse requires you
to shift up a half step. This is how the song is performed on the album 
version that I have (from a V/A collection called "Absolute Unforgettable")
and on the handful of live performances on YouTube.

So, with lyrics:
               Bb (x1333x@1)                  Cm (x3101x@1)      Cm7
      Oh, the shark, babe, has such teeth, dear
               F7 (131241@1)              Bb (x1333x@1)     And he shows them pearly whites
               Gm (355333@1)               Cm (x3101x@1)    Cm7
      Just a jackknife has old MacHeath, babe
               F7 (131241@1)                  Bb (x1333x@1)     And he keeps it out of sight.

Bb (x1333x@1)                  Cm (x3101x@1)       Cm7
      Ya know when that shark bites, with his teeth, babe
                F7 (131241@1)             Bb (x1333x@1)     Scarlet billows start to spread
              Gm (355333@1)                     Cm (x3101x@1)         Cm7
      Fancy gloves, though, wears old MacHeath, babe
                  F7 (131241@1)                   Bb (x1333x@1) F#7(Transition (242352@1)to verse 3)
      So there's never, never a trace of red.

From here on out, each verse is one half step higher than the previous one. 
Simply shift everything up one fret and keep on swingin'! F#7 (or whatever 
the chord may be, depending on where you are in the song) should provide a
comfortable transition into the next verse. For those interested in the big
picture, the song begins in Bb and ends in Eb.

Here are the rest of the lyrics:

Now on the sidewalk, Sunday mornin'
      Lies a body just oozin' life
      And someone's sneakin' 'round the corner
      Could that someone be Mack the Knife?
 
      There's a tugboat down by the river dontcha know
      Where a cement bag's just a'droopin' on down
      Oh, that cement is just, it's there for the weight, dear
      Five'll get ya ten, old Macky's back in town.
 
      Louie Miller, he disappeared, babe
      After drawin' out all his hard-earned cash
      And now MacHeath spends just like a sailor
      Could it be our boy's done somethin' rash?

Now Jenny Diver, oh Sukey Tawdry       
      Oh Miss Lotte Lenya and old Lucy Brown 
      Oh, the line forms on the right, babe
      Now that Macky's back in town.

I said Jenny Diver, whoa, Sukey Tawdry
      Look out to Miss Lotte Lenya and old Lucy Brown
      Yes, that line forms on the right, babe
      Now that Macky's back in town.

Look out old Macky is back!!

Comments, suggestions, and corrections are welcome.