The Baggies have had a torrid campaign so far, winning just three of their 27 fixtures in the top flight, which has left the club rooted to the bottom of the table.
The club are seven points adrift of safety following a four-game winless league run, with the most recent match ending in a 3-0 defeat to Chelsea.
Rather than sack manager Alan Pardew, the Baggies have taken aim at those responsible for the day-to-day running of the club.
A statement on West Brom's official website read: "Chairman John Williams and chief executive Martin Goodman have been given notice of termination of their contracts and have been placed on garden leave with immediate effect.
"Following his recent appointment as a director of WBA Holdings, the club's controlling company, Mark Jenkins is returning to be the football club's CEO.
"These changes follow Albion's poor results this season which currently sees the club at the bottom of the Premier League."
Jenkins had been West Brom's chief executive for 14 years.