The club are acting with conviction after seeing the team slip to rock bottom of the Premier League after a dire campaign so far, with manager Alan Pardew winning just one game since replacing Tony Pulis in November.
"There is much to do but for now the focus must exclusively be on the remaining games of this season", said Jenkins, who was previously chief executive at the club for 14 years.
A club spokesman told the club's website: "We would like to thank John and Martin for all their efforts since their appointments and wish them well for the future".
Perhaps taking inspiration from an old Brian Clough adage, table-propper-uppers West Brom have today sacked not their manager, but their chairman.
The Midlands club made a bright start to the current season with victories in their first two games before going 20 games without a win.More news: Pyeongchang Winter Olympics pairs skaters from the US
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The Telegraph reports that despite the boardroom changes Pardew remains safe for now, although his "methods and management are understood to be causing some friction within the squad".
But he's returned to steady the ship after his successor Goodman was sacked alongside chairman Williams and will now run the club until the end of the season.
The Baggies, who lost 3-0 on Monday to Chelsea, are seven points from safety with 11 matches left to play.
Albion, a Premier League side for the past eight years, return to action on Saturday with an FA Cup last-16 tie against Southampton.