The 22-year-old, who initially joined the south Yorkshire club on loan for the latter stages of last season, has now signed a four-year deal at Hillsbrough after becoming surplus to requirements under Brian McDermott.
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He told the Owls' official website: "I have been waiting patiently for this move all summer and I am so pleased it has gone through. Everything comes to those who wait.
"Wednesday fans have been encouraging me all summer to sign and they have played a massive part in this move."
His new manager, Dave Jones, says that bringing in the dynamic winger, who scored five goals in 14 appearances while on loan, shows that his side are moving forward.
"We're delighted to bring him here because he wants to do well," Jones told BBC Sheffield. "We're building and I wasn't brought here to consolidate this club. I was brought here to move it forward. This signing shows our ambition."
However, the former Cardiff City boss warns the fans that they should expect too much from the promising youngster.
"He's nowhere near the finished article but there's a lot of talent there to work with," he noted.