The 56-year-old Scot was appointed boss in June following the exit of Pepe Mel and was on a 12-month rolling contract.
The Baggies are 16th in the Premier League table, a point above the relegation zone following their 2-0 defeat at Stoke on Sunday - their seventh loss in nine games.
Irvine, who has previously been academy coach and assistant manager at Everton either side of spells as manager of first Preston and then Sheffield Wednesday is the 7th manager at West Brom in just over five years. He has officially been placed on gardening leave.
The Midlands club say they expect to be able to name Irvine's successor by the weekend.
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.
"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."
Irvine follows quickly after the sacking of Neil Warnocj by Crystal Palace at the weekend.
West Brom travel to West Ham on New Year's Day with Rob Kelly, assisted by fellow assistant head coach Keith Downing, in caretaker charge.