His assistants Graeme Jones and Wayne Jacobs were also relieved of their duties.
"This has been an enormously difficult decision for a club which will always hold Darren in such high regard," chief executive Mark Jenkins said.
"He took over at a very difficult time last season and reunited the club, a contribution that will never be forgotten."
He added: "Unfortunately Darren has not been able to engineer the consistency of form and results to convince the board that this objective (of returning to the Premier League) would be met."
The Baggies are fourth following the latest setback in their bid for promotion to the Premier League. They lost to promotion rivals Sheffield United and Leeds United prior to Saturday's disappointment against Ipswich, and are nine points adrift of the automatic promotion places.
Moore has recently drawn criticism for his decision to field Dwight Gayle out wide while Jay Rodriguez operates as the lone central striker. Former loanee Harvey Barnes was called back to Leicester City in January, but West Brom's case for an instant return to the top rung was seemingly strengthened by the temporary acquisitions of Jefferson Montero, Jacob Murphy, Mason Holgate, and Stefan Johansen this winter.
Moore initially took charge of West Brom last April when Alan Pardew was removed from the helm. The West Midlands outfit appeared destined for relegation, but Moore gave the club hope with an undefeated April which included a 1-0 win at Manchester United. However, they ultimately dropped into the Championship in early May.
First-team coach James Shan has been appointed as caretaker manager, but the club has vowed to name a new head coach "as soon as possible."
West Brom's next three matches are against Swansea City, Brentford, and Birmingham City.