Following a slow start to the campaign, new boss Irvine managed to win over supporters by leading the Baggies to their current position of 14th place in the Premier League table.
Mowbray, who spent just under three years in charge at The Hawthorns, believes that chairman Jeremy Peace deserves huge credit for appointing the Scot.
"I know Alan, he is a very, very good man and an honest and hard-working coach," the Birmingham Mail quotes the 50-year-old as saying. "I am delighted he has got this opportunity now because I know he has had discussions with Albion in the past.
"He has got good footballers and a good structure at the club and it won't be through a lack of work ethic or knowledge if Albion do not achieve their aims.
"I wish him well and I also wish the chairman well because of his visionary way of doing things. He must look at his club now and see it as no longer a yo-yo club between the Premier League and the Championship. That's a big achievement."
West Brom return to action a week on Monday when they host Manchester United.