I have altered Robin Young/yourxtuesday's Diana Krall version to get very close to the 
Julie London original

Cry Me a River: Julie London
As heard by John Uriel

INTRO:
(b d)Em9 chromatic run ? Am7 ? C ? B7 run down

Em9  Em6 Em maj7 Em7
Now  you say you're lonely
Am7            D13  D7#5  Gmaj7  F#m7
   You cry the long night through
B7               Em7
   Well, you can cry me a river
A9
   Cry me a river
Am7          D7    Am7/D G6  F#m7  B7
   I cried a river over  you

Em9  Em6 Em maj7 Em7
Now  you say you're sorry
Am7          D13 D7#5  Gmaj7 F#m7
   For being so  untrue
B7               Em7
   Well, you can cry me a river
A9
   Cry me a river
Am7          D7    Am7/D G6 Em6 F#7
   I cried a river over  you

Bm6               F#7           Bm6     F#7
   You drove me, nearly drove me, out of my head
 Bm6            Em6     F#7 F#(#5)
While you never shed a tear
Bm6               F#7           Bm6     F#7
 Remember, I remember, all that you said
   B                           Bmaj7 B7
   Told me love was too plebeian

F#m7                 B7
   Told me you were through with me and

Em9  Em6 Em maj7 Em7
Now  you say you love me
Am7              D13   D7#5  Gmaj7  F#m7
   Well, just to prove you  do
B7             Em7
   Come on and cry me a river
A9
   Cry me a river
Am7          D7    Am7/D G6 B7#5 B7
   I cried a river over  you
Am7          D7    Am7/D G6 B7#5 B7
   I cried a river over  you
Am7          D7    Am7/D G6  B7
   I cried a river over  you
OUTRO:
(b d)Em9 chromatic run ? Am7 ? C ? B7 run down