Redfearn, who took charge of the first team for the 2-1 loss at Charlton following the sacking of Neil Warnock, has been chiefly employed as the club's lead Under-21/pro-development coach.
The 47-year-old's first-team role will see him work alongside McDermott's assistant Nigel Gibbs.
"I want Nigel and Neil to be together with myself," McDermott told the Leeds official website.
"(Under-18's coach) Richard Naylor and Leigh Bromby are here at the training ground as well and they are both good people. I hadn't met Richard before, but he is a good man.
"I'm really pleased with the whole environment to be honest. Everyone wants to go in the same direction and that's important. What I won't be involved in is a blame culture, moaning, or gossiping. I have no interest.
"I won't do anything to the detriment of the football club."