The 52-year-old has signed a three-year deal with the former European Cup runners-up who will be hoping he can take them back to the top flight for the first time since they were relegated in 2004.
"Obviously the immediate aim is a return as soon as possible to the Premiership," David Haigh, deputy chief executive of GFH Capital which owns Leeds, said on the club's website (www.leedsunited.com).
"Brian's success in taking Reading to the Premiership last year was a key factor in our decision to hire him."
It is a goal that will have to wait until at least next season as McDermott takes over with Leeds in 17th place in the Championship, five points above the relegation zone with five games to play.
The appointment of McDermott comes after the club, beaten by Bayern Munich in the 1975 European Cup final, parted company with Neil Warnock earlier this month.
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