Wildsmith, a product of the club's academy, has made 18 appearances for the Owls in all competitions.
The 21-year-old had a loan spell with then-League One side Barnsley in 2015, making two appearances.
"I'm delighted to sign for the club long term, it's great that the club believe in me and see me as part of the future," he told the club website.
Sheffield Wednesday goalkeeper Joe Wildsmith has signed a new deal to stay with the Championship side until 2022.