“Irvine leaves the club with immediate effect and has been placed on gardening leave,” said a statement on the club’s official website.
It explained that the decision had been taken with “regret but necessity” and that they expect to name Irvine’s replacement by the weekend.
The club lie 16th in the league, just one point above the bottom three.
Assistant head coach Rob Kelly will take charge of the team for their New Year’s Day game at West Ham.
Albion’s technical director Terry Burton said: “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.
“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,” he added.