"I am very grateful to Rene, Alan and Ray, as well as Mick and Jonathan, for their commitment to Fulham," Fulham chairman Shahid Khan said in a statement.
"Their efforts were admirable and appreciated, and I wish them the best.
"Felix has come to Fulham with purpose and exceptional confidence, and I know he is extremely pleased to have Tomas Oral and Werner Leuthard join him for the mission ahead.
"From today forward, the focus is singularly on winning football matches and remaining in the Barclays Premier League. The work has begun."
Magath's first game comes away at West Brom this Saturday - one of 12 matches left remaining for the bottom-placed Cottagers, who lie four points adrift of safety.