The Owls decided not to renew the former Chelsea player's contract at the end of the 2019-20 season, and he joined Greek side Pafos as a free agent but his unhappy spell ended at Christmas when his contract was terminated.
Wednesday took the opportunity to resign the 31-year-old on a deal until the end of the season, but with an automatic one-year renewal if he played sufficient games in the second half of the campaign.
He started 22 of the last 23 matches, switching between central midfield and central defence.
Hutchinson and captain Barry Bannan are the only two out-of-contract players whose return to Hillsborough for next season has been confirmed, with the futures of a dozen others still to be decided.
Wednesday will play in League One next season, having been relegated on the final day of the Championship campaign.
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