The winger, who played for Iran in the World Cup, made 49 appearances for Fulham and scored six goals during a two-year spell at Craven Cottage.
Manager Felix Magath said: "Having spoken with Ashkan, we decided in the best interest of both Fulham and himself, that he would leave the club.
"During his time with us, he made some good appearances and scored some memorable goals, however we decided to part ways.
"It will always be our policy to have players who are committed to the club and have a desire to work for the common goal. We wish him very much luck for the future at Al-Arabi."
Dejagah has signed a four-year contract with Al-Arabi worth a reported £80,000-a-week.
Ali Barat, who brokered the deal, confirmed that Al-Arabi have paid a fee of 4.5m euros for his signature.
"There was a great deal of interest in Dejagah, but Al Arabi were determined to get him," Barat said.
"Ashkan has signed a four-year deal deal and it is a good deal for both clubs."