The 23-year-old moved to Pride Park from League One newcomers Exeter for an undisclosed fee, signing a three-year contract.
Clough, who crossed swords with Moxey in the Conference when he was manager of Burton, said: "Dean is a very exciting player that we have known about for some time.
"He will bring a lot of hunger and desire. His attitude and character are spot on and he has expressed his aspiration to improve and fight for a place in our team.
"He is versatile and will provide us with cover down the left, either in defence or midfield."