The Hawthorns outfit slipped to 16th in the Premier League – just two points above the relegation zone – after losing 1-0 at Cardiff City.
The result extended their winless record to six matches, while West Brom's 2-0 victory over Crystal Palace last month is the club's only triumph in any competition since September.
The decision is effective immediately and means Clarke – who took over from now-England boss Roy Hodgson at West Brom in June last year - is the fourth Premier League manager to lose his job this season.
West Brom sporting and technical director Richard Garlick said Clarke's team had not performed to the levels required in 2013, a year in which they have won just eight of 38 matches in all competitions.
"We have reluctantly come to the decision to relieve Steve of his duties after very careful consideration," Garlick told the club's official website.
"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.
"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.
"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. 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.
"We now begin the search to find a new head coach who will work within our existing structure, which has been in place for the past six years."
Clarke's assistant, Kevin Keen, has also been placed on gardening leave and Garlick thanked the pair for their contributions.
"On behalf of the board, I would like to thank Steve and Kevin for their efforts over the past 18 months," he said.
"We wish them and their families well for the future."
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
