The 55-year-old Scot has signed a 12-month rolling contract with the Premier League club.
West Brom had been looking for a new head coach since Pepe Mel stepped down from his role at The Hawthorns at the end of last season.
Irvine will join the Baggies once he has agreed to leave his position as Everton's academy coach.
The former winger spent two years as manager of Preston North End before joining Sheffield Wednesday in 2010. However, he was sacked by the Owls after 13 months in charge in February 2011.
"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," technical director Terry Burton told the club's official website.
Tim Sherwood had been tipped to take over at West Brom, but it is understood that he could not agree personal terms with the club.