The former centre-back was promoted from the role of Gunners' academy manager following Pat Rice's departure at the end of last season.
"Steve is really good to work with, especially for defenders as he has been a defender himself," Vermaelen told the club's official website.
"He knows what it is all about and gives us a lot of tips. He works a lot on the shape of the team and that is very important, so I am very happy he came to work with the first team."
Bould won nine trophies during a successful 11-year spell as a player with Arsenal before leaving in 1999.