Marseille, who will play their last league game of the season at Ajaccio on Saturday, will finish third behind champions PSG and second-placed RC Lens.
"We have respected Igor Tudor's wish not to continue with the club. Now it's his turn to communicate," said the club president on Thursday.
"On a personal note, and on behalf of the club, I'd like to say thank you for the work you've done, with a great deal of respect," Longoria told reporters.