Boro admitted last week that West Brom had made an approach for the 33-year-old defender who started his career at the Hawthorns.
Reports suggest that Ehiogu met with West Brom officials over the weekend and agreed terms. It is believed that the deal could be tied up in the next 24 hours.
Manager Bryan Robson has been silent over Ehiogu's move and rumours that Jimmy Floyd Hasselbaink could also be on his way to the West Midlands.