The 39-year-old will move to The Hawthorns on January 1, bringing an end to his three-and-a-half year association with the Grecians, for whom he has made 56 appearances since joining in 2006 from Boston.
Exeter manager Paul Tisdale said: "We are always sad to see a player leave us and Andy is no different. He's been a great asset to us, both in his role as general manager and also when called upon for the first team.
"Andy has always been a safe pair of hands and with more than 20 years of experience he's been fantastic in bringing on Paul (Jones) and Artur's (Krysiak) development here.
"It's no surprise to us that he's got a job at a Premiership side and I'm sure he will a huge success there."
Source: PA
Source: PA