The Baggies boss has paid the price for a run of seven defeats in nine Barclays Premier League games which has left the team in 16th place, a point above the bottom three.
The last straw was Sunday's 2-0 loss at Stoke, a third defeat in a row.
The club said in an official statement that Irvine had been placed on garden leave and assistant head coach Rob Kelly, with Keith Downing, would take charge of the team for the New Year's Day game at West Ham.
Albion technical director Terry Burton: "We appointed Alan in the summer convinced that we had taken on one of the foremost coaches in the UK and nothing that has happened since then has altered our view.
"The individual progress of our players such as Craig Dawson and Saido Berahino are testament to that.
"But sadly that simply has not translated into results and they remain the ultimate currency of Alan's position.
"Securing a sixth season in the Premier League is the over-riding target and sometimes unpleasant decisions have to be taken to serve that imperative.
"Alan has impressed everyone with his manner, dedication and diligence but he knows that results have simply not been good enough.
"We place on record our gratitude for his efforts and hold nothing but good wishes for his future endeavours. This was a decision taken with regret but sadly driven by necessity."