The 52-year-old has signed a three-year contract and will be given the instant task of guiding the club away from relegation trouble.
Warnock left Elland Road 11 days ago following the home defeat to Derby, while a run of four straight losses has seen Leeds slip to within five points of the Championship bottom three with five games remaining.
Last Saturday's 1-0 defeat at Charlton under caretaker Neil Redfearn was their fourth in a row, rendering Saturday's home game with Sheffield Wednesday a crucial one to their hopes of avoiding any late-season drama.
He steered Reading to the Championship title last season as the Berkshire club won 15 of their last 19 matches to reach the top flight for only the second time in their history.
McDermott, named Premier League manager of the month for January, becomes the club's fifth permanent manager in just over five years.
"We are delighted to have appointed Brian as our manager," said Leeds director David Haigh in a statement.
"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."