Former Manchester United coach Meulensteen was appointed head coach under Martin Jol, only to take control of first-team duties on 1 December following his compartiot's sacking.
However, with the bottom-placed west Londoners four points adrift of Premier League safety, chairman Shahid Khan has wielded the axe again.
Magath has been installed as first-team manager on an 18-month contract, with Meulensteen confirming his exit from the club despite the club statement not mentioning his name.
German manager Magath arrives at Craven Cottage with an impressive CV, having led Bayern Munich to successive Bundesliga titles in 2005 and 2006, before achieving the same feat with Wolfsburg in 2009.
"Felix is an accomplished manager with multiple honours in the Bundesliga and a hunger to replicate his success with Fulham in the Barclays Premier League.
"I'm especially impressed with the reputation Felix has for coming into clubs at difficult times, often late in the season, and lifting them to their potential and beyond.
"Felix knows that is precisely the task awaiting him at Fulham, and he made it abundantly clear that he wants and is ready for the opportunity.
"Our club has shown promise in recent matches, but the fact is we have not won a league match since 1 January.
"Given our form, we can no longer merely hope that our fortunes will finally turn. And with 12 matches remaining and at least four points separating us from safety, we certainly can no longer post empty results. Action was required.
"[Chief executive] Alistair Mackintosh did a wonderful job during the January transfer window to improve our club.
"This week, Alistair recommended Felix, with his history of producing results for clubs with similar challenges as ours, as the new manager of Fulham.
"Alistair's recommendation received my complete approval and Felix has my unequivocal support."
While Fulham are bottom of the Premier League and four points adrift of safety, the decision to sack Meulensteen with only 12 matches remaining has taken the football world by surprise.
Last Sunday the Dutchman led the Whites to a 2-2 draw at Manchester United and on Wednesday his side put in an impressive performance against Liverpool, only for the league's in-form side to win 3-2 thanks to a stoppage-time penalty.
Meulensteen was informed of the decision by chief executive Alistair Mackintosh and believes the decision to press the "panic button" was wrong.
"I am very, very surprised, very disappointed, very frustrated as well, because the job that I stepped into was one that took me by surprise from the start, because that was not anticipated with Martin Jol leaving and obviously you then have to step into situation which is not the best," he told BBC Radio 5 Live.
"You need to try and make things better as soon as you can, but you're playing with a deck of cards that are not yours.
"I haven't really been given any time to make that work. I thought the performance against Manchester United and Liverpool were very, very good and it was unfortunate that we did not pick up the points that we deserved.
"Twelve games to go, plenty of points to play for and I'm sure we would have turned it around.
"I've not been told anything. I knew the owners were freaking out and panicking about the fact that Fulham could get relegated, but they've had that sort of attitude already ten games back.
"They've hit the panic button on emotions of fear, but hey-ho, that's what happens in football. It's not always fair."