The Yorkshire side sacked Peter Jackson in March, with Gerry Murphy acting as caretaker.
"Andy has a track record of achieving promotion and took Barnsley into the Championship as recently as last season," said Terriers chairman Ken Davy.
"While we all know there are no guarantees in sport, the reality is that Andy has experience, a track record and the determination which we believe are necessary to help Huddersfield Town achieve its ambitions.
"In addition to managerial success, we believe his record as a player will command respect from the most experienced players as well as our up-and-coming stars.
"Andy is fully aware of our ambitions as a club, the first of which is to achieve promotion to the Championship."