The attacker has been linked with Juventus and the Premier League this summer.
"Jovetic will stay with us next season and the new team will be built around him to entertain the public," said Fiorentina communications chief Gianfranco Teotino.
"In the city there is great enthusiasm, as seen from the presentation of the new shirt and the positive number of season ticket sales. [New Coach Vincenzo] Montella has great enthusiasm and some innovative training methods.
"There is great confidence in our future and we want Stevan to be a part of our project and it is down to us to convince him to play at least one more year with us."