Last month, Moore was named as a temporary replacement for Alan Pardew and the club's youth coach guided the Baggies to 11 points from six matches in the Premier League.
West Brom were still relegated from the top flight, but the 44-year-old received the backing of the club's first-team squad and has allegedly been chosen for the position ahead of Brentford's Dean Smith.
Moore told the club's official website: "I am obviously extremely proud to accept this role and also extremely excited.
"We have a big summer ahead of us, a lot of hard work we need to get in now. I'm going all out to try to get those plans and personnel in place to make sure we've got everything ready.
"We need to be because this is a tough league packed with great clubs, but what an opportunity for us to move the club in the right direction."
West Brom have not stated the length of Moore's deal, but say that the contract is "improved and extended".