The 30-year-old, who enjoyed a successful loan spell at United in the second half of the 2014-15 season, has signed a two-year deal with the option of a third year after Leeds agreed a undisclosed fee with Palermo.
The fee is understood to be a considerable one, with former sporting director Nicola Salerno – whose official departure from the club was confirmed yesterday – helping to broker the deal.
Rosler said: “I am delighted to get such an experienced player to our squad.
“Of course, I think he has the experience of the league and British football and he has performed very well.
“He brings fantastic qualities with him (in terms of) what we are looking for. He can be a leader by himself for the young team he is working with.
“He brings a lot of qualities in terms of what we are looking for and also what we have because in general, we do not have the tallest team. We need somebody with a lot of qualities in the air.”