Here's a sheet music version from The Songs of George & Ira Gershwin Vol 1 (Warner). The chords are not dissimilar from those already posted (allowing for transposition), but there is an extra verse.

Mick

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SOMEONE TO WATCH OVER ME
(George and Ira Gershwin)

(Eb)There's a saying (Ebmaj7)old that (Eb9)love is blind, (Eb7)
(Abmaj7)Still we're often (Cm7)told, "seek and (F7)ye shall find."
(Fm7)So I'm going to seek a certain (Gm)lad (Bb7)I've (Eb)had (Fm7 Edim)in (Fm7b5)mind.(Bb7)

(Eb)Looking every-(Ebmaj7)where, haven't (Eb9)found him yet; (Eb7)
(Abmaj7)He's the big af-(Cm)fair I can-(F7)not forget.
(Fm7)Only man I ever think of (Gm)with (B7)re-(Eb)gret. (Ab Eb D7b9)
(Gm)I'd like to (C)add his initial to my (Gm)monogram. (C7)
(Bb)Tell (Bb6)me, (Cm7)where is the (F7)shepherd for (Bb)this (Ab)lost (Gm)lamb? (Bb7)

(She)
(Eb)There's a somebod-(Eb7)y I'm (Ab6)longing to (Abdim)see, (Eb)I hope that (Ebdim)he
(Bb7)Turns out to (Bbdim)be (Fm)some-(C7)one (Fm)who'll (Am7b5)watch (Fm7)ov-(Bb7)

er (Eb)me. (G7#5 Ab Bb7)
(Eb)I'm a little (Eb7)lamb who's (Ab6)lost in the (Abdim)wood. (Eb)I know I (Ebdim)could
(Bb7)Always be (Bbdim)good (Fm)to (C7)one (Fm)who'll (Am7b5)watch (Fm7)o-(Bb7)ver (Eb)me. (Eb7 Ab Bb7)

(Eb)Although he (Ab)may not be the man some girls think of as (Eb)handsome.
To (D7)my (D7#5)heart, (D7)he (G7)carries the (C)key. (C7 F7 Bb7)

(Eb)Won't you tell him (Eb7)please, to (Ab6)put on some (Abdim)speed, (Eb)follow my (Ebdim)lead,
(Bb7)Oh how I (Bbdim)need (Fm)some-(C7)one (Fm)to (Am7b5)watch (Fm7)o-(Bb7)ver (Eb)me. (Eb7 Ab G7#5 Fm7 Bb7#5)

(He)
There's a somebody I've wanted to see, I hope that she
Turns out to be someone who'll watch over me.
I'm a little lamb who's lost in the wood. I know I could
Always be good to one who'll watch over me.

She may be far she may nearby; I'm promising hereby
To my heart, she'll carry the key

And this world would be like heaven if she'd follow my lead,
Oh, how I need someone to watch over me.