The Scot will succeed Pepe Mel, who left the club by mutual consent the day after the Barclays Premier League season finished last month, once he "signs off" from his current role as Everton's academy manager.
Rob Kelly, who worked under Irvine at Preston and Wednesday, has also been appointed joint assistant head coach, alongside Keith Downing.
Albion technical director Terry Burton told the club's official website: "I'm delighted we have been able to secure the services of Alan and Rob."
The Baggies had been heavily linked with former Tottenham coach Tim Sherwood and Saturday's news may be slightly underwhelming for Baggies fans, given Irvine's lack of management experience in the top flight.
The Glaswegian was sacked at both Preston and Wednesday, who were relegated to League One under his tenure, and he has not taken charge of a club since leaving Hillsborough in 2011.
However, he has played a prominent role at Everton, helping to bring through the likes of Ross Barkley and Jack Rodwell to the senior team.
And the Baggies are now convinced they have the set-up in place - with Dean Kiely remaining as goalkeeping coach - to improve on last season's 17th-placed Premier League finish.
Burton added: "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."
Former Birmingham and Newcastle boss Chris Hughton and ex-West Ham boss Gianfranco Zola were among the other rumoured candidates to replace Mel.
The Spaniard left after a little more than five months at the Hawthorns after only narrowly avoiding relegation from the top flight, and he never appeared to win the wholesale support of the midlands club's hierarchy.