Milenkovic, who played all three of Serbia's matches at Euro 2024, has 57 international caps and made 216 Serie A appearances for Fiorentina, reaching the Europa Conference League final with them in May.
"We have long admired his performances with the Serbian national team, and in Serie A and European competitions for Fiorentina," Forest's chief football officer Ross Wilson said in a statement.
"He is a key part of our squad planning this summer and I know how enthusiastic he has been to join."
Forest host Bournemouth in their first Premier League match of the season on August 17th.
