The Premier League outfit made the decision in the wake of the Baggies' 1-0 defeat to Cardiff City away from home on Saturday.
"This was the unanimous decision of the football club's board of directors following a disappointing performance throughout 2013," read a statement on West Brom's official website.
"Albion have won only seven of their 34 Barclays Premier League games during the calendar year – a 20% win percentage yielding a total of only 31 points – despite a substantial investment in the first-team squad.
"Joint-assistant head coach Keith Downing will assume control of first-team affairs whilst the club considers all available options for a new head coach."
Clarke's assistant Kevin Keen has also been placed on gardening leave.
West Brom are currently 16th in the league table with 15 points from 16 matches, just two points above the relegation zone.