Bannan, who has made 447 appearances for the club, had been out of contract before signing the deal.
He told the club website, external: “I’m delighted to get it done and I can look forward again.
“I’ve made it clear over the years my love for the club and the love I receive back.
“This club is a big part of me and my family. With the season getting closer, this last week has been tough because there was interest from elsewhere and I had a lot to think about.”
The Owls are due to kick-off their new Championship season against Leicester City on Sunday, 10 August.