Rosler follows Brian McDermott, Dave Hockaday, Darko Milanic and most recently Neil Redfearn, whose contract as head coach finished at the end of the season.
"This is a chance of a lifetime at a great club with great potential," the 46-year-old former East Germany striker Rosler told a news conference.
"It doesn't get much bigger than this, it was a no-brainer."
Leeds, English champions in 1969, 1974 and 1992, runners-up in the 1975 European Cup and Champions League semi-finalists in 2001, finished 15th in the second tier this season.
(Reporting by Michael Hann; Editing by Ken ferris)
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