Black has been named Remi Garde's No2 at Villa.
Black joined Rotherham as first team coach last summer and had one game in charge as caretaker boss before becoming Redfearn's assistant manager.
Redfearn said: “He has had an opportunity that he felt he couldn't turn down and we fully appreciated that, so he goes with everyone's best wishes.
“We want to thank him for all his effort and hard work whilst with Rotherham United, and from a personal point of view I have thoroughly enjoyed working with him.
“Eric really bought into what I wanted to do here and was very popular with the players and staff.
“On behalf of everyone at the club I would like to wish Eric all the very best for the future."