The 23-year-old will see out the remainder of the 2013/14 season at the Weser Stadion, before linking up with his new team-mates in the summer.
"We are delighted that the transfer's gone through," enthused Eintracht sporting director Bruno Hübner. "At 23, Aleksandar already has considerable experience and is incredibly versatile. He can play in defensive midfield or as a full-back."
Belgrade-born Ignjovski spent two years on loan at 1860 Munich, before joining die Grün-Weißen from OFK Beograd in August 2011. To date, he has scored one goal in 58 Bundesliga appearances.