Schwarzer was offered a new deal to stay at the Riverside Stadium and had also been linked to Bayern Munich in Germany as well as a possible move to Italy.
"After stiff competition from a number of high-profile European clubs, I am exceptionally pleased that Mark has chosen to come to Fulham," added Hodgson.
"His credentials in both the domestic and international arenas are impeccable, which is reinforced by the calibre of clubs that wanted to sign him."
Fulham escaped relegation to the Championship on the last day of the season.
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