The 19-year-old was out of contract at the conclusion of last term, in which Fulham were relegated from the Premier League.
The highly rated Tankovic – a Sweden international and a prolific scorer for Fulham at youth level – made three league appearances last season but did not feature after February as the Craven Cottage outfit battled relegation.
"Unfortunately Fulham was in a difficult position (last season)," Tankovic told AZ's official website.
"Fighting against relegation, the coach opted for older players.
"In three years, I've learned a lot, but for me it was about time to leave. In this club I can learn from a legend like (coach) Marco van Basten.
"I play to entertain. I create opportunities for others, but I prefer to score even more. The last two seasons I became top scorer of Fulham's Under-21 (team)."
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