Mepham moves to the Baggies in a permanent transfer and has signed a three-year contract.
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"Chris brings a wealth of Premier League and Championship experience to the dressing room, including being part of a play-off winning team last season," Albion sporting director Andrew Nestor said.
"At 27, he offers additional quality to a revamped defensive unit, comprising a balance of players in their prime and in development years who all offer versatility across the back line."
Mepham has moved to the Hawthorns for around £1m.