The club announced via their Twitter feed that the 46-year-old German had signed a two-year contract following talks at Elland Road on Tuesday and he becomes Massimo Cellino's 5th head coach since the controversial Italian became owner in April 2014.
Neil Redfearn is still under contract until June 30 and had the option of resuming as academy manager, but it remains to be seen whether he has severed all ties with the club after his public stand-off with Cellino.
Cellino has branded former academy manager Redfearn as "weak" and a "baby" since returning to office earlier this month after serving a Football League ban for a tax conviction in his homeland last year.
Rosler, a former striker with Manchester City, was sacked by Wigan in November 2014 after less than a year in the job.
He had guided Wigan to the Championship play-offs and the semi-finals of the FA Cup the previous season, but departed after the club had slipped into the relegation zone.
Rosler started out in management in Norway in 2004 with Lillestrom, Viking Stavanger and then Molde before returning to England to take charge of Brentford in June 2011.
He guided the Bees to within minutes of automatic promotion to the Championship on the final day of the regular 2012/13 season before a last-gasp defeat to Doncaster.
Brentford went on to lose the play-off final to Yeovil and Rosler left the club the following December to take charge of the Latics.
Cellino hired 36 coaches during 22 years as owner of Cagliari and his latest move will fuel the fire in the bellies of his many detractors among Leeds fans, whose numbers have swelled in recent months.
Boyhood Leeds fan Redfearn, hugely popular among the club's supporters, spent six years in charge of the academy before being appointed head coach by Cellino following the sacking of Darko Milanic in October 2014.
Redfearn, 49, steered the club away from relegation trouble in the Sky Bet Championship and played a key role in bringing through the club's latest batch of academy players.
Despite the unexplained sacking of assistant Steve Thompson in early April and a catalogue of off-field distractions under Cellino's tenure, Redfearn has been widely recognised for retaining his dignity under testing circumstances.
Source : PA
Source: PA