The 50-year-old has been relieved of his managerial duties and placed on "gardening leave" following the Baggies' 1-0 away defeat to Cardiff City in the Premier League on Saturday.
"We have reluctantly come to the decision to relieve Steve of his duties after very careful consideration," Garlick said in a statement on 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.
"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. 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."
West Brom are currently 16th in the league table with 15 points from 16 matches, just two points above the relegation zone.