Reports suggested that former Tottenham manager Tim Sherwood had rejected the position after failing to agree personal terms, but a Baggies statement appeared to suggest that Irvine had been chosen on merit.
Irvine takes over at the Hawthorns following Pepe Mel’s departure at the end of the season.
"I'm delighted we have been able to secure the services of Alan and Rob,” said Albion technical director Terry Burton in a statement on the club website.
"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.”
In his 15-year playing career, Irvine represented Queen's Park in Scotland before spells with Everton, Crystal Palace, Dundee United and Blackburn Rovers.
He retired from playing in 1992 and since then has coached for 22 years in jobs with Newcastle, Blackburn, Preston and Sheffield Wednesday before joining Everton in 2011.
West Brom narrowly escaped relegation after finishing 17th in the Premier League last season.
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