Cutler, 36, who appeared for the likes of Coventry, Aston Villa, Stoke and Swansea during his playing career, will replace the retiring Mick Kearns at the Banks's Stadium.
"We're well aware of Neil's ability as a goalkeeping coach," said Smith.
"He comes here with a good reputation and as someone who is based locally, it's a perfect fit for him and the club.
"He's keen to work with all of the keepers at every level throughout the club and is extremely forward-thinking and enthusiastic about the role."
Cutler has previously worked as goalkeeping coach at Bury and latterly Scunthorpe, leaving Glanford Park at the end of last season.
"I'm delighted to be here," Cutler said. "I've had a good, long chat with Dean Smith and I'm happy to be joining a club that is going places.
"Dean is a top young manager and Richard O'Kelly is a great coach, so I can only learn from them."