The Baggies boss guided the club on an unbeaten run throughout the month, beating Manchester United and Newcastle United along the way.
Moore assembled all of his staff together at the West Brom training ground to share the plaudits after the award announcement was made.
"I'm delighted, it has been a wonderful joint effort by everyone here," he told the team's official website. "I stand here to collect the award but, as I've said before, it has been a joint effort by everyone at West Bromwich Albion Football Club.
"There has been unity here between all the departments of the club and together that has helped the players put the performances together on the pitch.
"Everyone knows my connection with the football club, I know everybody and everybody knows me.
"Together we're working and it's been good to see the transition over the past four or five weeks and long may that continue."