This is based on Earonoff's and Thohug's transcriptions, but with a few changes, 
especially to the bridge as it didn't sound quite right to me. I think this is a little closer.

This is also based on the version from the Muppet Album which is in 4:4 time, rather 
than the 3:4 time version in the movie.

G (320003@1)        Dsus/G    Em (022000@1)     AThis (x02220@1)looks familiar. Vaguely familiar
G (320003@1)       Dsus/G     Dsus/F#      Em (022000@1)         AAlmost (x02220@1)unreal, yet,       it's too soon too feel yet
Am (x02210@1)        D (xx0232@1)            Bm (x24432@1)   Esus (022200@1)EClose (022100@1)to my heart, and yet so far away
    Am (x02210@1)        D (xx0232@1)        GI'm (320003@1)going to go back there someday

G (320003@1)        Dsus/G   D (xx0232@1) Em (022000@1)          ASun (x02220@1)rises, Night falls, Sometimes the Sky calls
G (320003@1)          Dsus/G          Em (022000@1) AIs (x02220@1)that a song there? And do I belong there?
Am (x02210@1)       D (xx0232@1)             Bm (x24432@1)       Esus (022200@1)EI've (022100@1)never been there, but I know the way
    Am (x02210@1)        D (xx0232@1)        G (320003@1)                G/F#I'm (320002@1)going to go back there someday

Em (022000@1)         A (x02220@1)           DCome (xx0232@1)and fly with me. It's more fun to share
Em (022000@1)          Asus (x02230@1)    A (x02220@1) DWe're (xx0232@1)both be completely at home in mid-air
      E (022100@1)         C# (x43121@1)        F#m (244222@1)       F#m/E
We're flying, not walking, on featherless wings
       D (xx0232@1)       D/C# (x40232@1)     C (x32010@1)       Dsus (xx0233@1)   DWe (xx0232@1)can hold onto love, like invisible strings

G (320003@1)           Dsus/G       Em (022000@1)               AThere's (x02220@1)not a word yet for old friends you've just met
G (320003@1)             Dsus/G    Dsus/F#    Em (022000@1)         APart (x02220@1)heaven, part space.      Or have I found my place?
Am (x02210@1)         D (xx0232@1)          Bm (x24432@1)    Esus (022200@1)EYou (022100@1)can just visit, but I plan to stay
    Am (x02210@1)        D (xx0232@1)        G (320003@1)      G/F#Em
I'm going to go back there someday
    Am (x02210@1)        D (xx0232@1)        GI'm (320003@1)going to go back there someday