The 34-year-old Belgian lawyer, one of the most high-profile women in English football, had previously held a similar position at London club Charlton.
Meire, explaining her departure from Hillsborough, told Sheffield Wednesday's website: "Since joining Sheffield Wednesday in January 2018, I felt a warm welcome from everyone at the club and the fans at games and around the city.
"I would like to wish the chairman, the staff and players at the club all the very best," she added.
"With new manager Steve Bruce in charge and the fantastic support of our amazing fans, the club's journey to the Premier League has never looked any better."
Yorkshire club Wednesday are currently 16th in the Championship and 11 points adrift of the play-off places.
Meire faced widespread hostility from Charlton supporters during a three-year spell at the south London side from 2014-2017 that saw the club relegated to the third tier of English football amid unrest over Roland Duchatelet's ownership.
Fans took exception to being labelled as "customers" as they turned on Meire.
"It is not nice to read in the papers you are a horrible person, that you are horrible at your job, attacking my personality, attacking me as a whole," she told AFP in an interview published last week.