The result is the Baggies' fourth straight defeat and leaves them in 16th place in the Premier League table just two points above the relegation places.
A statement on the club's website said the decision was "unanimous" and due to a "disappointing performance during 2013" with the club winning just seven games in the calendar year despite significant investment in the squad.
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“It has been well documented that we have not had the rub of the green in certain games this season but that does not cloud the generally disappointing points return during this calendar year, culminating in today’s fourth-successive defeat at Cardiff.
“This club's track record proves we do not take such decisions lightly, having only enforced a change in this position three times in approximately 14 years.
“But with key games coming thick and fast, we felt it was important we acted now to give the club the best possible chance of a successful outcome this season.
“Our player wage bill is the highest in the club’s history and we feel we have built a squad capable of being very competitive in the Premier League.
"On behalf of the Board, I would like to thank Steve and Kevin for their efforts over the past 18 months. Garlick.
“We wish them and their families well for the future.”
Albion also confirmed that Kevin Keen has also been placed on gardening leave while Keith Downing will charge of the first-team in the meantime.