The former Baggies defender, 44, led them on an unbeaten run in April as caretaker manager after replacing Alan Pardew, with three wins and two draws.
But he was unable to save Albion, who were bottom of the Premier League and 10 points adrift when he took over.
Owner Guochuan Lai, chief executive Mark Jenkins and technical director Giuliano Terraneo agreed the appointment at a meeting this week.
Moore played for West Brom from 2001 until 2006, twice helping them to promotion to the Premier League.
After succeeding Pardew he oversaw 1-0 victories away at Manchester United and Newcastle, a home win over Tottenham and a draw against Liverpool.
He accrued 11 points from the 18 available after being named as caretaker manager and reeled in a 10-point gap to five points.
Once confirmed in the role, Moore will set about rebuilding a squad that is likely to lose a number of key players this summer, with the defender Jonny Evans and striker Salomon Rondon two of the players who can leave for cut-price fees.
In addition, Gareth McAuley, James Morrison and Boaz Myhill are all out of contract while Claudio Yacob has the option to extend for a further year.
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