The former Reading manager, who was sacked by the Royals in March, replaces Neil Warnock at Elland Road and will bring Nigel Gibbs as his right-hand man.
McDermott walks straight into a relegation battle, with Leeds now just five points clear of the Championship's bottom three following a run of three points from seven games.
But the club's owners are aiming higher than survival, and it was the Irishman's achievement of taking Reading into the Premier League which attracted the club's owners.
David Haigh, deputy chief executive of GFH Capital, said: "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 Premier League. Brian's success in taking Reading to the Premier League last year was a key factor in our decision to hire him."