Chief executive Mark Jenkins said in a statement on the club's website: "This has been an enormously difficult decision.
"He took over at a very difficult time last season and reunited the club, a contribution that will never be forgotten.
"But we have made it clear from the outset that everything this season was geared to making as swift a return to the Premier League as possible."
West Brom are fourth in the table on 61 points, nine points outside the top two automatic promotion spots but still in the thick of the battle for playoff places.
After a good start to the season, though, they have won just four of their past 12 league games and were held 1-1 at home by bottom club Ipswich Town on Saturday.
Moore, who played for West Brom between 2001-6, took charge of the team after the departure of manager Alan Pardew in April 2018 and was later appointed after leading Albion's valiant but ultimately doomed effort to avoid Premier League relegation.
(Reporting by Antony Lawrence; Editing by Ian Chadband)
