The 23-year-old has agreed a three-year contract with the Sky Bet Championship club.
Lees has made a total of 207 senior appearances throughout his career and has also International experience with England at U16 and U21 level.
The central defender told the club's official website: "We've been in talks and I've been hoping everything was OK and I'm delighted to have put pen to paper.
"You never know with any deal until it's signed, of course, and I couldn't be happier. This is a massive football club steeped in top-flight history for most of its existence and I can't wait to get started.
"I've spoken to plenty of players who have played for Sheffield Wednesday and they can't speak highly enough of the place.
"Obviously, that has a big bearing on your decision and it’s great that so many people in the game speak so well of this club."