Djordjevic, 26, will link up with Lazio after enjoying another impressive campaign.
The Serbia international played a key role in Nantes' promotion to Ligue 1 last term, scoring 20 goals in 34 Ligue 2 appearances.
And he has netted 10 top-flight goals in 26 outings this season, form that has helped Nantes away from the relegation zone.
Lazio announced the move on their official YouTube channel, with Djordjevic confirming the move via video link-up.
He said: "Hi guys, I am Filip Djordjevic the new player of Lazio in (the) upcoming season.
"I am very happy and excited about joining such a big club. And I hope that we will have great moments all together."
Djordjevic is likely to replace Germany veteran Miroslav Klose, who appears set to leave Lazio at the end of this season.
