The primary justification as I recall was WMD and the letter that some dude at the CIA wrote up at Kinko's supposedly confirming Saddam's purchase of Nigerian yellowcake - a theory about as sound as those Nigerian spam mails I get.
The letter was signed by a Nigerian diplomat. Problem is, that diplomat retired some three years prior to the date of the letter (god help us).
Bush laid the groundwork for the attack in his State of the Union address and I'd be hard pressed to find the Saddam-Osama link in its text. It was pretty well known that Osama didn't care much for Saddam since he's not much of a Muslim and ran a secular government. Now, the idea that Atta met up with an Iraqi intel agent gained some traction in the talk show curcuit but I don't think that had much to do with it.
Basically, justification be damned, I think W's mind was made up probably before he took office and he was just looking for an excuse and he was dumb enough to believe those clowns who advise him.