The Serbian international will join the Italian club on a free transfer, having spent almost seven years at Les Canaries.
"I congratulate Filip; he has been at Nantes for six and a half years, he's our longest-serving player and he has given everything for the club," said Kita, according to the official Ligue 1 website.
"We've tried for the last eighteen months to extend his contract, but some very big clubs threw their hats in the ring.
"It's completely normal that Filip move on to seek new challenges."
Nantes currently occupy 13th position in the Ligue 1 table on 36 points.