The Northern Ireland Under-19 international, who skippered Wednesday's Under-18 side this season, has put pen to paper on a one-year deal.
"I couldn't be happier," Hanna told the club's official website. "To sign for a club the size of Sheffield Wednesday is a dream come true.
"I have worked really hard to get to this stage of my career and will continue that hard work moving forward."
The 18-year-old has represented Northern Ireland at both Under-18 and Under-19 level.