But the appointment of the German head coach is a controversial one.
Wagner performed miracles when he guided Huddersfield into the Premier League back in 2017. He then kept them there for a year.
But the Express & Star understands the 49-year-old was not the number one choice of the club's board - with his managerial career having stalled since keeping the Terriers up.
Instead, the Baggies hierarchy wanted to appoint former Sheffield United manager Chris Wilder.
That decision was vetoed however by owner Guochuan Lai.
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