I've sat in my room many hours with my amp cranked up to acheive this tone. It was almost impossible to nail, but this is pretty close. Note that for this tone to sound almost perfect, your strings need to be fairly new, and perfectly in tune, or else you'll get an undesired grainy sound.
Turn your amp to the Crunch setting to imitate the 69 fender amps, which Eric often uses. Turn the drive all the way up, and experiment by barely turning it down until it sounds correct on your amp.
Treble - 0. This is one of the most suprising things, because most people think he has high treble, but really, his lows and mids create his sound.
Mid - 9:00 O'clock - 9:10 position.
Low - 10 O'clock - 10:10 position.
Next turn your Tape Echo to the Twelve o-clock position, which should be Right between the E in tape, and the E in Echo, then take it and turn it just a hair more. Set the echo to around 190 BPM.
Turn your guitars tone down to 6 - 7, and use the treble pickup. Turn todn your guitar volume to about 7, and turn up your amp. I'm using an Epiphone Les Paul Ultra 2, and this tone sounds amazing.
Note that you will have to play around with your settings a bit, but don't move any knob more than a hair or you'll kill the sound. EJ's tone is very precise and very unstable on the Spider III, so the smallest adjustments can ruin the sound.