The 26-year-old, who has scored 10 goals for Nantes in 26 Ligue 1 appearances this term, announced he would move to the Serie A club on a free transfer in a video posted on Lazio's official YouTube channel.
He said: "Hello, I am Filip Djordjevic. I am a new Lazio player for next season.
"I am very excited about playing for such a prestigious club. I hope we can experience great emotions together."
Djordjevic joined Nantes from Red Star Belgrade in 2008 and has played nine times for Serbia, scoring four goals.