The Everton academy boss will take on his new role following the conclusion of his contract at Goodison Park.
Baggies assistant head coach Keith Downing will remain at the club, but will also be joined by Rob Kelly - who comes with Irvine from Everton.
"I'm delighted we have been able to secure the services of Alan and Rob," West Brom technical director, Terry Burton, told the club's official website.
"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 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."