The 52-year-old was expected to be named as Neil Warnock's successor following reports that he had entered advanced talks with the Championship outfit this week.
McDermott, who spent 12 years at Reading, has only been out of work for a brief stint since getting dismissed from the Madejski Stadium due to the Royals' dismal state in the relegation zone of the Premier League.
Deputy chief executive of GFH Capital David Haigh told the club's official website: "We are delighted to have appointed Brian as our manager. He is a man with a proven track record of success and shares our vision of the best way to return long terms and sustainable success to this great football club.
"Obviously the immediate aim is a return as soon as possible to the Premiership. Brian's success in taking Reading to the Premiership last year was a key factor in our decision to hire him."
The club have also confirmed that McDermott and assistant Nigel Gibbs will take charge of the team with immediate effect, which suggests that the coach will be on the touchline for this Saturday's clash against Sheffield Wednesday.