The veteran had hinted he would reconsider his next step after taking North Macedonia to the UEFA EURO 2020 tournament.
His contract with Genoa had already expired and he turned 38 last month.
However, his form at the Euros and in Serie A last season convinced him to carry on for one more year.
Pandev has 101 goals and 56 assists in 473 Serie A appearances through his career.
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