Mark Jenkins, a director of West Brom's controlling company WBA Holdings, returns to the club as CEO having previously held the position for 14 years, and he highlighted the importance of results in the Premier League following his appointment.
"There is much to do, but for now the focus must exclusively be on the remaining games of this season", Jenkins said.
"We would like to thank John and Martin for all their efforts since their appointments and wish them well for the future", a club spokesperson said.
The sackings come with West Brom bottom of the Premier League and seven points from the safety line following Monday's 3-0 defeat at Chelsea, with the club citing poor results as a catalyst for change.
Since Watford sent Marco Silva packing last month the Premier League Sack Race has been dominated by two managers: Antonio Conte and Mauricio Pellegrino.
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The Baggies are bottom of the league on 20 points from 27 games.
With West Brom now seven points adrift of safety in the Premier League, it seems highly unlikely that the Baggies will now be giving too much thought to their transfer plans for the next window.
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.
However, he has failed to revive the faltering Baggies and has won just one of his 13 matches in charge.
They have some respite from their league woes this weekend when they face fellow strugglers Southampton in the FA Cup.