Tankovic joined the London outfit in 2011 when he was 16 years of age and made his debut for the Cottagers in the 2013/14 campaign.
The 19-year-old Swede featured in three Premier League games for Fulham, but was not offered a new contract when his original deal ran out.
Dutch club AZ have now recruited Tankovic on a contract that runs until June 2019.
AZ have also signed Guus Hupperts from Roda JC, who suffered relegation from the Eredivisie at the end of last season.
The 22-year-old winger cost the Alkmaar-based club for approximately €1million and has signed a contract that runs until June 2018.