The 42-year-old has moved to Villa Park where he will link up with Dean Smith – who he previously worked under when the pair were at Walsall.
Albion head coach Darren Moore said: “We tried everything to persuade Neil to stay but he enjoyed a very strong working relationship with Dean from their past connections and felt a strong pull to work with him again.
“We wish him well and thank him for his efforts.”
Mark Naylor, Albion’s professional phase development coach, will now train the senior goalkeepers while the club assess its options.
Technical director Luke Dowling added: “Mark has stepped up to this role before and performed admirably and we have every confidence he will do so again.
“We will also consider options to ensure the best outcome for the club.”