Irvine, who has also managed Preston North End, left his position as academy coach with the Toffees to take charge at The Hawthorns.
"The situation at this club is similar to what I went through at Everton when I went there with David," the Sheffield Telegraph quotes him as saying. "I've got a great deal of respect for the club right the way from the first team through to the academy.
"It is run very sensibly and, as a result of that, any head coach coming in has got a great chance of doing a good job. A number of the players who have had success in the Premier League with the club are still here.
"But it's a small squad at this moment in time and, clearly, the first job is going to have to be to get some more players in."
Irvine has signed a 12-month rolling contract with West Brom.