The midfielder, regarded as one of Ireland's finest young talents, has signed a three-year deal with the Owls.
He played almost 100 games for UCD, scoring 14 goals, and recently earned a recent call-up to the Republic of Ireland U21 squad for their Euro 2013 qualifier against Turkey.
Corry was offered a contract by Burnley as an 18-year-old but opted to stay in Ireland and was widely scouted by English clubs last season.
He said: "I have bided my time for the right move at the right time and this is it for me. Sheffield Wednesday is a club with a huge heritage and history and the stadium just blows you away.
"I really can't wait to get started and, like everyone else at the club, I have ambitions of playing in the Premier League.
"But it's one step at a time, I know it will be difficult at first but once I settle in and get my sharpness, I have the confidence in my ability to do well for Sheffield Wednesday."
