Here are the chords. I just copied from what he strums when he played live in a video from 2001.
I think some variations were used but this is im sure 100% there
Sleeping - Rick Astley
Tuning:EADGBe Capo None
[022033]
[032033]
[000323]
[224432]
Sleeping x4
I Toss And Turn, I'm Turning Round
But I Cannot Sleep
I'm Hypnotized, I'm Paralysed
By A Different Beat
I Hear Your Voice, Getting Louder Now
Yet So Out Of Reach
But I'm Mistaken It's Only The Echo Of You
((Repeat Chord Pattern))
And I'm Not Sleeping Now That You're Gone
I Can't Help Feeling I Did You Wrong
And The Night Goes, On And On And On And On
A Crowded Bar, The Mating Game
I'm So Out Of Place
It's So Bizarre, She's Coming On To Me
But I See Your Face
The DJ Plays, Familiar Songs
And It Takes Me Back
But I'm Mistaken It's Only The Echo Of You
And I'm Not Sleeping Now That You're Gone
I Can't Help Feeling I Did You Wrong
And I Need Healing It's Been So Long
And The Night Goes, On And On And On And On
I Hear Your Voice, I Hear Your Voice Calling
I Hear Your Voice, I Hear Your Voice Calling