The Scotland international midfielder joined the Baggies just minutes before the closure of the transfer window for £1.2million and has signed a three-and-a-half-year deal at The Hawthorns.
"I always liked Nigel when he played for QPR, Portsmouth and Southampton. He is an intelligent player, has good stamina and is a very good passer of the ball," Baggies boss Bryan Robson said."He has got the experience now of relegation fights and playing in the Premiership. I just feel he will improve our squad. "I just felt we have been a bit short in midfield. Riccardo Scimeca and Lloyd Dyer had gone during January and it is a matter of balancing the squad all the time and just trying to improve as you keep doing that."