Winkler, 49, had been at Oakwell since Daniel Stendel took charge of the League One club in June.

Winkler worked alongside Siewert during the latter's spell as manager of Rot-Weiss Essen between 2015 and 2016.

"We're disappointed to see Andreas leave the club, because he was a strong member of staff," Barnsley chief executive Gauthier Ganaye said.

Barnsley say Huddersfield, who appointed Siewert to replace David Wagner earlier this week, have paid "substantial compensation" for Winkler's services.

Coach Dale Tonge will to replace Winkler at Oakwell, with Stendel looking a the possibility of appointing another coach from Germany in due course.