Gacinovic last season captained FK Vojvodina Novi Sad in the Serbian league.
"We have managed to win a hugely talented player for us," said Eintracht sports director Bruno Huebner in a statement. "He is quick and agile and already has a lot of experience for his age. It is an investment for the future."
The German league kicks off this week with Eintracht travelling to last season's runners-up VfL Wolfsburg on Sunday.
(Reporting by Karolos Grohmann; editing by Amlan Chakraborty)
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