The 60-year-old German, who succeeded the sacked Rene Meulensteen in February, was charged with keeping the Whites in the Premier League but watched them tumble into the Championship with defeat at Stoke at the weekend.
The former Bayern Munich, Schalke and Wolfsburg boss signed an 18-month contract when he took over and vowed to rebuild an ageing squad after their 13-year stay in the top flight was ended.
And a Fulham spokesperson told Sky Sports on Wednesday: "Felix will manage the club next season. There has never been any ambiguity over his future from our perspective. He wants to bring us back to the Premier League."
Magath, who became the Whites' third manager of the campaign after they sacked Martin Jol and replaced him with Meulensteen in December, picked up three vital victories against Newcastle, Aston Villa and Norwich to take the club to within two points of safety last month.
But he was forced to apologise for a woeful performance in the 4-1 defeat on Saturday - their 24th loss of the season.
In a statement on the club's official website on Tuesday, Magath said: "I was appointed by Mr Shahid Khan realising that there was a distinct possibility that we would not survive.
"I was not only brought in until the end of the season with the primary target of keeping Fulham in the Premier League, but to build a team that can compete in the top flight. My commitment and desire to Fulham remains.
"During the summer months there most certainly will be many changes within the club. We obviously need to improve and redefine our playing staff, and we have in our academy team some talented, young and hungry players.
"I have experienced on many occasions, through working and developing youth team players, that they have the possibility to become top professionals. I am looking forward to the task ahead and to a successful future for all of us."