Irvine, 55, moves from his current role as Everton’s academy manager and he fills the vacancy left by Pepe Mel’s departure at the end of the season.
His appointment comes, according to Sky sources, after Tim Sherwood turned the job down after failing to agree personal terms.
Irvine is bringing Rob Kelly to work as joint assistant head coach alongside Keith Downing, whilst Dean Kiely will remain as the club’s goalkeeping coach.
Albion's technical director Terry Burton told the club's website: "I'm delighted we have been able to secure the services of Alan and Rob.
"With the support of Keith and Dean, we firmly believe we have put in place the right coaching team to move the club forward.
"From the outset, we decided to pursue candidates who are renowned for their coaching ability and Alan was very much at the forefront of our thoughts because of his achievements in the Premier League and the high regard he is held within the game.
"In the end it came down to two outstanding candidates for the role.
“But, following a detailed recruitment process, we decided Alan and the team around him are best suited to tackle the challenges we face in the Barclays Premier League.
“He has a vast knowledge from grassroots up thanks to the roles he has performed during his decades in the game and knows what it takes through good and testing times.”
Irvine has been manager of Everton’s academy since July 2011 and has helped developed players such as Ross Barkley and Jack Rodwell.
He had similar roles with Newcastle and Blackburn Rovers before managing Preston North End and then Sheffield Wednesday.
As a player, Irvine started his 15-year career with Scottish side Queen’s Park in 1977 before playing for Everton, Crystal Palace, Dundee United and finally Blackburn.