Saric and two other associates - one of whom is still on the run - were sentenced to between 11 and 20 years in prison by a special organised crime court in Belgrade.
Three other defendants who enjoy protected witness status were sentenced to between five and 10 months.
Saric, 44, was charged with masterminding a trafficking ring between 2007 and 2009 which smuggled drugs from South America to Europe.
Saric was eventually arrested in Latin America in March 2014 before he was transferred to Belgrade where he pleaded not guilty to the charges.
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Saric's lawyers say they intend to challenge today's verdict.
Serbia in 2013 opened an inquiry into suspected links between top officials and members of organised crime groups after the press reported that Ivica Dacic, when he was interior minister, had met a Saric accomplice in 2008.
Serbia lies on the so-called Balkans route used by criminals to smuggle people, drugs and weapons to western Europe.
The European Union has made cracking down on the drugs trade one of the key conditions for Balkan nations' membership of the EU. Serbia launched accession talks in January 2014.