Irvine worked alongside Paul Lambert at Blackburn Rovers last season but after he became available after Lambert's exit from Ewood Park, Alex Neil has suggested that he wasted little time in appointing his fellow Scot as first-team coach.
Neil told the club's official website: "Alan has worked with some top managers in his time, as well as having been a manager himself.
"He will bring a wealth of experience gained over the course of his career. It adds to us as a coaching team because he's had real success at clubs.
"In terms of what we've got we're now more diverse. He's got a great reputation but also has the willingness and drive to be here, which is great."
Irvine has also had coaching spells with Everton and Newcastle United, while he was manager of West Bromwich Albion as recently as 2014.