The 25 year old Nigerian internation has joined West Brom after 2 and half years with the Millers.
In a spell that was fruitful for both player and club, the defender gained his first call up to the Nigerian squad and earned promotion at Wembley via the play off's,
In all, Semi made 98 appearances for the Millers and scored 12 goal.
The fee has not been disclosed, but is reported to be around the 1.3m mark.